Finite Group Databasebeta

← #19212227

Subgroups — #19212227

Order 5888.

500 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675855C211yesmaximal, characteristic
2#15673539C211yesmaximal, characteristic, complemented
3#15673141C211yesmaximal, characteristic, complemented
4#15671220C211yesmaximal, characteristic, complemented
5#15671217C211yesmaximal, characteristic
6#15671217C211yesmaximal, characteristic
7C23×#1271C211yesmaximal, characteristic, complemented
8C2×#10625064C411yescharacteristic
9C2×#10625063—21no—
10C2×C8×Dic23—21no—
11#13092319C2211yescharacteristic
12#13092318C411yescharacteristic
13#13092316C411yescharacteristic
14#13092309—21no—
15#13092307—21no—
16C4⋊C4×Dic23C411yescharacteristic
17#13092264—21no—
18C42×Dic23C2211yescharacteristic
19#13092172C2211yescharacteristic
20#13092172C2211yescharacteristic
21#13092171—21no—
22#13092171—21no—
23#13092171—21no—
24C23×#389C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D92C2×C411yescharacteristic
28C22×C4×D23—21no—
29C22×C8×C23—21no—
30C22×C8×C23—21no—
31C2×C4⋊C4×C23—21no—
32C2×C4⋊C4×C23C2×C411yescharacteristic
33C2×C4⋊C4×C23C2×C411yescharacteristic
34C2×C42×C23C2311yescharacteristic
35C2×(C2×D23)⋊C4—21no—
36C2×(C2×D23)⋊C4—21no—
37C2×(C2×D23)⋊C4—21no—
38C2×(C2×D23)⋊C4—21no—
39C2×(C2×D23)⋊C4—21no—
40C2×C4⋊Dic23—21no—
41C2×C4⋊Dic23C2×C411yescharacteristic
42C2×C4×Dic23—21no—
43C2×C4×Dic23C2×C411yescharacteristic
44C2×C4×Dic23C2×C411yescharacteristic
45C2×C4×Dic23D411yescharacteristic
46C2×C4×Dic23D411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C2×C4×Dic23D411yescharacteristic
49C22×C23⋊C8—21no—
50C22×C23⋊C8—21no—
51#10625064—22no—
52#10625064C814yescomplemented
53#10625063—42no—
54#10625063—42no—
55C23×#95—21no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58C8×Dic23—24no—
59C23×D23—21no—
60C22×C4×C23—21no—
61C22×C4×C23—21no—
62C22×C4×C23C22×C411yescharacteristic
63C22×C4×C23C2×D411yescharacteristic
64C22×C4×C23C2×D411yescharacteristic
65C22×Dic23—21no—
66C22×Dic23C22⋊C411yescharacteristic
67C22×Dic23C22⋊C411yescharacteristic
68C22×Dic23C22⋊C411yescharacteristic
69C22×Dic23C22⋊C411yescharacteristic
70C2×D92—21no—
71C2×D92—41no—
72C2×D92—41no—
73C2×D92C2×C812yes—
74C2×C4×D23—24no—
75C2×C4×D23—42no—
76C2×C4×D23—42no—
77C2×C8×C23—22no—
78C2×C8×C23—41no—
79C2×C8×C23—41no—
80C2×C8×C23—41no—
81C2×C8×C23—41no—
82C2×C8×C23—41no—
83C4⋊C4×C23—21no—
84C4⋊C4×C23—41no—
85C4⋊C4×C23—41no—
86C4⋊C4×C23—41no—
87C4⋊C4×C23C2×C812yes—
88C42×C23—41no—
89(C2×D23)⋊C4—24no—
90(C2×D23)⋊C4—42no—
91(C2×D23)⋊C4—41no—
92(C2×D23)⋊C4—41no—
93(C2×D23)⋊C4—41no—
94(C2×D23)⋊C4—41no—
95(C2×D23)⋊C4—42no—
96C4⋊Dic23—42no—
97C4⋊Dic23—41no—
98C4×Dic23—21no—
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—22no—
103C4×Dic23—41no—
104C4×Dic23—41no—
105C4×Dic23—42no—
106C4×Dic23C2×C812yes—
107C4×Dic23M1612yes—
108C2×C23⋊C8—22no—
109C2×C23⋊C8—41no—
110C2×C23⋊C8—41no—
111C2×C23⋊C8—41no—
112C2×C23⋊C8—41no—
113C2×C23⋊C8—41no—
114#7580—231nomaximal, Sylow
115C23×C23C2×C22⋊C411yescharacteristic
116C22×D23—22no—
117C22×D23—41no—
118C22×D23—41no—
119C22×D23—41no—
120C22×D23—41no—
121C22×D23—41no—
122C22×D23—41no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—22no—
130C2×C4×C23—41no—
131C2×C4×C23—41no—
132C2×C4×C23—41no—
133C2×C4×C23—41no—
134C2×C4×C23—41no—
135C2×C4×C23C22×C811yescharacteristic
136C2×C4×C23C2×M1611yescharacteristic
137C2×C4×C23#13511yescharacteristic
138C2×C4×C23#13511yescharacteristic
139C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—41no—
151C2×Dic23—41no—
152C2×Dic23—41no—
153C2×Dic23C22⋊C812yes—
154C2×Dic23C22⋊C812yes—
155C2×Dic23#10412yes—
156D92—42no—
157D92—42no—
158C4×D23—48no—
159C8×C23—42no—
160C8×C23—81no—
161C23⋊C8—42no—
162C23⋊C8—81no—
163#2293—231no—
164#1839—231no—
165#1744—231no—
166#1271—231no—
167#1271D2311yescharacteristic, complemented
168#1270—231no—
169#1270—231no—
170C22×C23C2×C22⋊C811yescharacteristic
171C22×C23#41011yescharacteristic
172C22×C23#41311yescharacteristic
173C22×C23#41611yescharacteristic
174C22×C23#41811yescharacteristic
175C22×C23C2×#10411yescharacteristic
176C22×C23#42111yescharacteristic
177C2×D23—42no—
178C2×D23—42no—
179C2×D23—42no—
180C2×D23—81no—
181C2×D23—81no—
182C2×D23—81no—
183C2×D23—81no—
184C4×C23—21no—
185C4×C23—21no—
186C4×C23—21no—
187C4×C23—21no—
188C4×C23—21no—
189C4×C23—21no—
190C4×C23—42no—
191C4×C23—81no—
192Dic23—22no—
193Dic23—22no—
194Dic23—22no—
195Dic23—41no—
196Dic23—81no—
197C2×C4×D4—231no—
198C2×#117—461no—
199C2×C4×C8—461no—
200#390—231no—
201#390—231no—
202#389—231no—
203#389C2×D2311yescharacteristic
204#388—461no—
205#388—461no—
206C4×C4⋊C4—231no—
207C4×C22⋊C4—461no—
208C43—231no—
209#336—231no—
210#336—231no—
211#336—461no—
212#336—461no—
213#336—461no—
214#336C2×D2311yescharacteristic
215#336C2×D2311yescharacteristic
216C2×C23#145811yescharacteristic
217C2×C23#147611yescharacteristic
218C2×C23#147811yescharacteristic
219C2×C23#150511yescharacteristic
220C2×C23#152111yescharacteristic
221C2×C23#153211yescharacteristic
222C2×C23#155311yescharacteristic
223D23—82no—
224C22×D4—231no—
225C23×C4—461no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—461no—
229C22×C8—461no—
230C4×D4—234no—
231C4×D4—462no—
232#117—922no—
233#117—922no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—231no—
236C2×C4⋊C4—461no—
237C2×C4⋊C4C4×D2311yescharacteristic
238C2×C4⋊C4C4×D2311yescharacteristic
239C2×C22⋊C4—461no—
240C2×C22⋊C4—461no—
241C2×C22⋊C4—461no—
242C2×C22⋊C4—461no—
243C2×C22⋊C4—461no—
244C2×C42—231no—
245C2×C42—231no—
246C2×C42—231no—
247C2×C42—231no—
248C2×C42—231no—
249C2×C42—231no—
250C2×C42—461no—
251C2×C42C22×D2311yescharacteristic
252C4×C8—464no—
253#95—21no—
254#95—461no—
255#95—461no—
256C23#758011yescharacteristic, complemented, Sylow
257C24—461no—
258C2×D4—232no—
259C2×D4—461no—
260C2×D4—921no—
261C2×D4—921no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—231no—
265C22×C4—231no—
266C22×C4—231no—
267C22×C4—231no—
268C22×C4—464no—
269C22×C4—461no—
270C22×C4—922no—
271C22×C4—922no—
272C22×C4C2×C4×D2311yescharacteristic
273C22×C4D4×D2311yescharacteristic
274C22×C4D4×D2311yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—462no—
282C2×C8—921no—
283C2×C8—921no—
284C2×C8—921no—
285C2×C8—921no—
286C2×C8—921no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—921no—
292C4⋊C4—922no—
293C4⋊C4C8×D2312yes—
294C22⋊C4—464no—
295C22⋊C4—922no—
296C22⋊C4—922no—
297C22⋊C4—921no—
298C22⋊C4—921no—
299C22⋊C4—921no—
300C22⋊C4—921no—
301C42—41no—
302C42—232no—
303C42—232no—
304C42—462no—
305C42—461no—
306C42—461no—
307C42—461no—
308C42—461no—
309C42—921no—
310C42—921no—
311C42—922no—
312C23—462no—
313C23—921no—
314C23—921no—
315C23—921no—
316C23—921no—
317C23—921no—
318C23—921no—
319C23C22⋊C4×D2311yescharacteristic
320D4—922no—
321D4—922no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—232no—
335C2×C4—232no—
336C2×C4—232no—
337C2×C4—461no—
338C2×C4—461no—
339C2×C4—461no—
340C2×C4—461no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—461no—
344C2×C4—461no—
345C2×C4—461no—
346C2×C4—928no—
347C2×C4—921no—
348C2×C4—921no—
349C2×C4—921no—
350C2×C4C2×C8×D2311yescharacteristic
351C2×C4M16×D2311yescharacteristic
352C2×C4#1062508211yescharacteristic
353C2×C4#1062508511yescharacteristic
354C2×C4#1062508711yescharacteristic
355C2×C4#1062509011yescharacteristic
356C8—42no—
357C8—81no—
358C8—922no—
359C8—1841no—
360C22—922no—
361C22—922no—
362C22—922no—
363C22—1841no—
364C22—1841no—
365C22—1841no—
366C22—1841no—
367C22C22⋊C8×D2311yescharacteristic
368C22#1309238911yescharacteristic
369C22#1309240011yescharacteristic
370C22#1309241211yescharacteristic
371C22#1309242011yescharacteristic
372C22#104×D2311yescharacteristic
373C22#1309243211yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—81no—
382C4—462no—
383C4—462no—
384C4—462no—
385C4—921no—
386C4—1841no—
387C2—1842no—
388C2#1567171011yescharacteristic
389C2#1567177811yescharacteristic
390C2#1567178611yescharacteristic
391C2#1567190311yescharacteristic
392C2#1567197311yescharacteristic
393C2#1567201611yescharacteristic
394C2#1567210111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7580
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. #15673539C2semidirect
3. #15673141C2semidirect
4. #15671220C2semidirect
7. C23×#1271C2semidirect
52. #10625064C8semidirect
167. #1271D23semidirect
256. C23#7580semidirect