Finite Group Databasebeta

← #19212247

Subgroups — #19212247

Order 5888.

510 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675940C211yesmaximal, characteristic
2#15673539C211yesmaximal, characteristic, complemented
3#15673245C211yesmaximal, characteristic, complemented
4#15671223C211yesmaximal, characteristic, complemented
5#15671217C211yesmaximal, characteristic
6#15671217C211yesmaximal, characteristic
7C23×#1272C211yesmaximal, characteristic, complemented
8C2×#10625118C411yescharacteristic
9C2×Q8×Dic23C411yescharacteristic
10C2×#10625064C411yescharacteristic
11C2×Dic23⋊C8—21no—
12C2×C8×Dic23—21no—
13#13092319C2211yescharacteristic
14#13092309—21no—
15#13092309—21no—
16#13092282C411yescharacteristic
17#13092264—21no—
18#13092264—21no—
19C42×Dic23C2211yescharacteristic
20#13092172C2211yescharacteristic
21#13092172C2211yescharacteristic
22#13092171—21no—
23#13092171—21no—
24C23×#391C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×Q8×C23C2×C411yescharacteristic
28C22×D92C2×C411yescharacteristic
29C22×C4×D23—21no—
30C22×C8×C23—21no—
31C22×C8×C23—21no—
32C2×C4⋊C4×C23C2×C411yescharacteristic
33C2×C42×C23C2311yescharacteristic
34#10625118—22no—
35#10625118C814yescomplemented
36Q8×Dic23—42no—
37C2×(C2×D23)⋊C4—21no—
38C2×(C2×D23)⋊C4—21no—
39C2×(C2×D23)⋊C4—21no—
40C2×(C2×D23)⋊C4—21no—
41C2×(C2×D23)⋊C4—21no—
42C2×C4⋊Dic23—21no—
43C2×C4⋊Dic23C2×C411yescharacteristic
44C2×C4×Dic23—21no—
45C2×C4×Dic23C2×C411yescharacteristic
46C2×C4×Dic23C2×C411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C2×C4×Dic23D411yescharacteristic
49C2×C4×Dic23D411yescharacteristic
50C2×C4×Dic23D411yescharacteristic
51C22×C23⋊C8—21no—
52C22×C23⋊C8—21no—
53#10625064—42no—
54C23×#95—21no—
55C23×#95—21no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58Dic23⋊C8—24no—
59C8×Dic23—42no—
60C23×D23—21no—
61C2×Q8×C23—21no—
62C2×Q8×C23—41no—
63C2×Q8×C23—41no—
64C2×Q8×C23C2×C812yes—
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
74C22×Dic23C22⋊C411yescharacteristic
75C2×D92—21no—
76C2×D92—41no—
77C2×D92—41no—
78C2×D92C2×C812yes—
79C2×C4×D23—42no—
80C2×C4×D23—42no—
81C2×C4×D23—42no—
82C2×C8×C23—22no—
83C2×C8×C23—41no—
84C2×C8×C23—41no—
85C2×C8×C23—41no—
86C2×C8×C23—41no—
87C2×C8×C23—41no—
88C4⋊C4×C23—41no—
89C42×C23—41no—
90(C2×D23)⋊C4—24no—
91(C2×D23)⋊C4—24no—
92(C2×D23)⋊C4—41no—
93(C2×D23)⋊C4—41no—
94(C2×D23)⋊C4—41no—
95(C2×D23)⋊C4—41no—
96(C2×D23)⋊C4—42no—
97C4⋊Dic23—42no—
98C4⋊Dic23—41no—
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—22no—
104C4×Dic23—22no—
105C4×Dic23—41no—
106C4×Dic23—42no—
107C4×Dic23C2×C812yes—
108C4×Dic23M1612yes—
109C2×C23⋊C8—22no—
110C2×C23⋊C8—41no—
111C2×C23⋊C8—41no—
112C2×C23⋊C8—41no—
113C2×C23⋊C8—41no—
114C2×C23⋊C8—41no—
115#7584—231nomaximal, Sylow
116C23×C23C2×C22⋊C411yescharacteristic
117C22×D23—22no—
118C22×D23—41no—
119C22×D23—41no—
120C22×D23—41no—
121C22×D23—41no—
122C22×D23—41no—
123C22×D23—41no—
124Q8×C23—42no—
125Q8×C23—42no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—22no—
133C2×C4×C23—41no—
134C2×C4×C23—41no—
135C2×C4×C23—41no—
136C2×C4×C23—41no—
137C2×C4×C23—41no—
138C2×C4×C23C22×C811yescharacteristic
139C2×C4×C23C2×M1611yescharacteristic
140C2×C4×C23#13511yescharacteristic
141C2×C4×C23#13511yescharacteristic
142C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C23#13711yescharacteristic
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152C2×Dic23—41no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23C22⋊C812yes—
156C2×Dic23C22⋊C812yes—
157C2×Dic23#10012yes—
158C2×Dic23#10412yes—
159D92—42no—
160D92—42no—
161C4×D23—84no—
162C8×C23—42no—
163C8×C23—81no—
164C23⋊C8—42no—
165C23⋊C8—81no—
166C4×#124—231no—
167#1839—231no—
168C4×C4⋊C8—231no—
169#1272—231no—
170#1272D2311yescharacteristic, complemented
171#1270—231no—
172#1270—231no—
173C22×C23C2×C22⋊C811yescharacteristic
174C22×C23#41011yescharacteristic
175C22×C23C2×#10011yescharacteristic
176C22×C23#41611yescharacteristic
177C22×C23#41711yescharacteristic
178C22×C23C2×#10411yescharacteristic
179C22×C23#42111yescharacteristic
180C2×D23—42no—
181C2×D23—42no—
182C2×D23—42no—
183C2×D23—81no—
184C2×D23—81no—
185C2×D23—81no—
186C2×D23—81no—
187C4×C23—21no—
188C4×C23—21no—
189C4×C23—21no—
190C4×C23—21no—
191C4×C23—21no—
192C4×C23—21no—
193C4×C23—42no—
194C4×C23—81no—
195Dic23—22no—
196Dic23—22no—
197Dic23—22no—
198Dic23—22no—
199Dic23—81no—
200C2×#124—231no—
201C2×C4×Q8—231no—
202C2×C4×D4—231no—
203C2×C4⋊C8—461no—
204C2×C4×C8—461no—
205#391C2×D2311yescharacteristic
206#390—231no—
207#388—461no—
208#388—461no—
209#382—231no—
210C4×C22⋊C4—461no—
211C4×C22⋊C4—461no—
212C43—231no—
213#336—231no—
214#336—231no—
215#336—461no—
216#336—461no—
217#336C2×D2311yescharacteristic
218#336C2×D2311yescharacteristic
219C2×C23#146011yescharacteristic
220C2×C23#147611yescharacteristic
221C2×C23#147711yescharacteristic
222C2×C23#150911yescharacteristic
223C2×C23#152111yescharacteristic
224C2×C23#152711yescharacteristic
225C2×C23#155111yescharacteristic
226D23—82no—
227C22×Q8C4×D2311yescharacteristic
228C22×D4—231no—
229C23×C4—461no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—461no—
233C22×C8—461no—
234#124—234no—
235#124—462no—
236C4×Q8—922no—
237C4×D4—922no—
238C2×C4⋊C4—231no—
239C2×C4⋊C4—461no—
240C2×C4⋊C4C4×D2311yescharacteristic
241C2×C22⋊C4—461no—
242C2×C22⋊C4—461no—
243C2×C22⋊C4—461no—
244C2×C22⋊C4—461no—
245C2×C22⋊C4—461no—
246C2×C42—231no—
247C2×C42—231no—
248C2×C42—231no—
249C2×C42—231no—
250C2×C42—231no—
251C2×C42—231no—
252C2×C42—461no—
253C2×C42C22×D2311yescharacteristic
254C4⋊C8—464no—
255C4×C8—922no—
256#95—21no—
257#95—21no—
258#95—461no—
259#95—461no—
260C23#758411yescharacteristic, complemented, Sylow
261C24—461no—
262C2×Q8—21no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8C8×D2312yes—
266C2×D4—232no—
267C2×D4—461no—
268C2×D4—921no—
269C2×D4—921no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—231no—
273C22×C4—231no—
274C22×C4—231no—
275C22×C4—231no—
276C22×C4—461no—
277C22×C4—922no—
278C22×C4—922no—
279C22×C4—922no—
280C22×C4C2×C4×D2311yescharacteristic
281C22×C4D4×D2311yescharacteristic
282C22×C4D4×D2311yescharacteristic
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—462no—
290C2×C8—921no—
291C2×C8—921no—
292C2×C8—921no—
293C2×C8—921no—
294C2×C8—921no—
295C4⋊C4—41no—
296C4⋊C4—921no—
297C4⋊C4—922no—
298C22⋊C4—464no—
299C22⋊C4—464no—
300C22⋊C4—922no—
301C22⋊C4—921no—
302C22⋊C4—921no—
303C22⋊C4—921no—
304C22⋊C4—921no—
305C42—41no—
306C42—232no—
307C42—232no—
308C42—462no—
309C42—462no—
310C42—461no—
311C42—461no—
312C42—461no—
313C42—461no—
314C42—921no—
315C42—922no—
316C23—462no—
317C23—921no—
318C23—921no—
319C23—921no—
320C23—921no—
321C23—921no—
322C23—921no—
323C23C22⋊C4×D2311yescharacteristic
324Q8—42no—
325Q8—42no—
326D4—922no—
327D4—922no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—232no—
341C2×C4—232no—
342C2×C4—232no—
343C2×C4—232no—
344C2×C4—461no—
345C2×C4—461no—
346C2×C4—461no—
347C2×C4—461no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—461no—
352C2×C4—921no—
353C2×C4—921no—
354C2×C4—921no—
355C2×C4—1844no—
356C2×C4C2×C8×D2311yescharacteristic
357C2×C4M16×D2311yescharacteristic
358C2×C4#1062508511yescharacteristic
359C2×C4#1062508711yescharacteristic
360C2×C4#1062508911yescharacteristic
361C2×C4#1062509011yescharacteristic
362C8—42no—
363C8—81no—
364C8—922no—
365C8—1841no—
366C22—922no—
367C22—922no—
368C22—922no—
369C22—1841no—
370C22—1841no—
371C22—1841no—
372C22—1841no—
373C22C22⋊C8×D2311yescharacteristic
374C22#1309238911yescharacteristic
375C22#100×D2311yescharacteristic
376C22#1309241211yescharacteristic
377C22#1309241711yescharacteristic
378C22#104×D2311yescharacteristic
379C22#1309243211yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—462no—
389C4—462no—
390C4—462no—
391C4—462no—
392C4—1841no—
393C2—1842no—
394C2#1567171611yescharacteristic
395C2#1567177811yescharacteristic
396C2#1567178311yescharacteristic
397C2#1567192111yescharacteristic
398C2#1567197311yescharacteristic
399C2#1567199311yescharacteristic
400C2#1567209111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7584
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #15673539C2semidirect
3. #15673245C2semidirect
4. #15671223C2semidirect
7. C23×#1272C2semidirect
35. #10625118C8semidirect
170. #1272D23semidirect
260. C23#7584semidirect