Finite Group Databasebeta

← #19212312

Subgroups — #19212312

Order 5888.

588 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625101C211yesmaximal, characteristic
2#15673465C211yesmaximal, characteristic, complemented
3#15671219C212yesmaximal, complemented
4#15671217C212yesmaximal, complemented
5C23×#1797C211yesmaximal, characteristic, complemented
6C2×#10625101C411yescharacteristic
7C2×C4×D92C411yescharacteristic
8C2×C4×C22⋊D23—21no—
9C2×C22⋊(C23⋊C8)—21no—
10#13092319C2211yescharacteristic
11#13092315C2211yescharacteristic
12#13092308—21no—
13#13092296—21no—
14#13092277C411yescharacteristic
15C4×C4⋊Dic23C411yescharacteristic
16C4×(C2×D23)⋊C4—21no—
17#13092172—21no—
18#13092172C2212yes—
19C22×C42×C23C2211yescharacteristic
20C2×C23×C4⋊C8—21no—
21C2×C23×C22⋊C8—21no—
22C23×#336C2212yes—
23C23×C4×C23C2×C411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C23×C4×C23D411yescharacteristic
26C22×C22⋊D23—21no—
27C22×D92C2×C411yescharacteristic
28C22×C4×D23—21no—
29C22×C8×C23—22no—
30C2×C42×C23—42no—
31C2×C42×C23C2×C411yescharacteristic
32C2×C42×C23D411yescharacteristic
33C2×C42×C23D411yescharacteristic
34C2×C42×C23C2311yescharacteristic
35C2×C22⋊Dic23—21no—
36#10625101—22no—
37#10625101C814yescomplemented
38C4×C22⋊D23—44no—
39C2×(C2×D23)⋊C4—21no—
40C2×(C2×D23)⋊C4—21no—
41C2×(C2×D23)⋊C4—21no—
42C2×(C2×D23)⋊C4—21no—
43C2×C4⋊Dic23C2×C411yescharacteristic
44C2×C4⋊Dic23C2×C411yescharacteristic
45C2×C4⋊Dic23C2×C411yescharacteristic
46C2×Dic23⋊C4—21no—
47C2×C4×Dic23—21no—
48C22×C23⋊C8—22no—
49C4×D92—42no—
50C23×C4⋊C8—42no—
51C23×C22⋊C8—42no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C23⋊#95—21no—
55C22⋊(C23⋊C8)—42no—
56C24×C23C22⋊C411yescharacteristic
57C23×D23—21no—
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—21no—
61C22×C4×C23—21no—
62C22×C4×C23—41no—
63C22×C4×C23—41no—
64C22×C4×C23—41no—
65C22×C4×C23—41no—
66C22×C4×C23—41no—
67C22×C4×C23C22⋊C411yescharacteristic
68C22×C4×C23C22⋊C411yescharacteristic
69C22×C4×C23C22⋊C411yescharacteristic
70C22×C4×C23C2×C812yes—
71C22×C4×C23M1612yes—
72C22×C4×C23C22×C411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C22×C4×C23C2×D411yescharacteristic
75C2×C22⋊D23—24no—
76C2×C22⋊D23—42no—
77C2×C22⋊D23—42no—
78C22×Dic23—21no—
79C22×Dic23—21no—
80C22×Dic23—21no—
81C2×D92—21no—
82C2×D92—41no—
83C2×D92—41no—
84C2×D92C2×C812yes—
85C2×C4×D23—42no—
86C2×C4×D23—42no—
87C2×C4×D23—42no—
88C2×C8×C23—42no—
89C2×C8×C23—42no—
90C2×C8×C23—42no—
91C42×C23—22no—
92C42×C23—22no—
93C42×C23—41no—
94C42×C23—41no—
95C22⋊Dic23—42no—
96(C2×D23)⋊C4—24no—
97(C2×D23)⋊C4—42no—
98(C2×D23)⋊C4—41no—
99(C2×D23)⋊C4—42no—
100(C2×D23)⋊C4—41no—
101C4⋊Dic23—21no—
102C4⋊Dic23—41no—
103C4⋊Dic23—41no—
104C4⋊Dic23C2×C812yes—
105Dic23⋊C4—42no—
106C4×Dic23—42no—
107C2×C23⋊C8—42no—
108C2×C23⋊C8—42no—
109C2×C23⋊C8—42no—
110#7599—231nomaximal, Sylow
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—21no—
114C23×C23—21no—
115C23×C23—21no—
116C23×C23—21no—
117C23×C23C22⋊C812yes—
118C23×C23C2×C22⋊C411yescharacteristic
119C22×D23—22no—
120C22×D23—41no—
121C22×D23—41no—
122C22×D23—41no—
123C22×D23—41no—
124C22×D23—41no—
125C22×D23—41no—
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—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—42no—
140C2×C4×C23—42no—
141C2×C4×C23—44no—
142C2×C4×C23—42no—
143C2×C4×C23—42no—
144C2×C4×C23C22⋊C812yes—
145C2×C4×C23#9912yes—
146C2×C4×C23C22×C811yescharacteristic
147C2×C4×C23C2×M1611yescharacteristic
148C2×C4×C23AGL(1,ℤ/8)12yes—
149C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C23#13711yescharacteristic
151C22⋊D23—48no—
152C2×Dic23—22no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23—41no—
156C2×Dic23—41no—
157C2×Dic23—41no—
158C2×Dic23—41no—
159C2×Dic23—41no—
160C2×Dic23—41no—
161D92—42no—
162D92—42no—
163C4×D23—84no—
164C8×C23—82no—
165C23⋊C8—82no—
166C4×#121—231no—
167#1817—231no—
168#1797D2311yescharacteristic, complemented
169#1271—232no—
170#1270—232no—
171C22×C23—22no—
172C22×C23—22no—
173C22×C23—22no—
174C22×C23—41no—
175C22×C23—41no—
176C22×C23—41no—
177C22×C23—41no—
178C22×C23C2×C22⋊C811yescharacteristic
179C22×C23C2×#9911yescharacteristic
180C22×C23#41311yescharacteristic
181C22×C23#41711yescharacteristic
182C22×C23#41811yescharacteristic
183C22×C23#42111yescharacteristic
184C22×C23#42111yescharacteristic
185C2×D23—42no—
186C2×D23—42no—
187C2×D23—42no—
188C2×D23—81no—
189C2×D23—81no—
190C2×D23—81no—
191C2×D23—81no—
192C4×C23—21no—
193C4×C23—21no—
194C4×C23—22no—
195C4×C23—22no—
196C4×C23—22no—
197C4×C23—21no—
198C4×C23—21no—
199C4×C23—41no—
200Dic23—42no—
201Dic23—81no—
202Dic23—81no—
203C2×#121—231no—
204C2×C4×D4—231no—
205C2×C4×D4—461no—
206C22×C42C2×D2311yescharacteristic
207C2×C4⋊C8—21no—
208C2×C22⋊C8—21no—
209C2×C22⋊C8—461no—
210#390—231no—
211#389—231no—
212#388—461no—
213#386—461no—
214#380—231no—
215C4×C4⋊C4—231no—
216C4×C22⋊C4—461no—
217#336—232no—
218#336—461no—
219#336C2×D2312yes—
220C2×C23—42no—
221C2×C23#145911yescharacteristic
222C2×C23#147711yescharacteristic
223C2×C23#147811yescharacteristic
224C2×C23#151011yescharacteristic
225C2×C23#151311yescharacteristic
226C2×C23#153511yescharacteristic
227C2×C23#155711yescharacteristic
228D23—82no—
229C22×D4—231no—
230C22×D4—461no—
231C23×C4—461no—
232C23×C4C4×D2311yescharacteristic
233C23×C4D9211yescharacteristic
234C23×C4C22⋊D2311yescharacteristic
235C22×C8—22no—
236C22×C8—462no—
237#121—234no—
238#121—462no—
239C4×D4—922no—
240C4×D4—924no—
241C2×C4⋊C4—231no—
242C2×C4⋊C4—231no—
243C2×C4⋊C4—231no—
244C2×C4⋊C4—461no—
245C2×C22⋊C4—461no—
246C2×C22⋊C4—461no—
247C2×C22⋊C4—461no—
248C2×C22⋊C4—461no—
249C2×C22⋊C4—461no—
250C2×C42—42no—
251C2×C42—461no—
252C2×C42C4×D2311yescharacteristic
253C2×C42D9211yescharacteristic
254C2×C42C22⋊D2311yescharacteristic
255C2×C42C22×D2311yescharacteristic
256C4⋊C8—42no—
257C22⋊C8—42no—
258C22⋊C8—922no—
259#95—461no—
260#95—461no—
261#95—461no—
262C23#759911yescharacteristic, complemented, Sylow
263C24—461no—
264C24(C2×D23)⋊C411yescharacteristic
265C2×D4—232no—
266C2×D4—464no—
267C2×D4—461no—
268C2×D4—921no—
269C2×D4—921no—
270C2×D4—922no—
271C2×D4—922no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—461no—
282C22×C4—461no—
283C22×C4—461no—
284C22×C4—922no—
285C22×C4—922no—
286C22×C4—922no—
287C22×C4C8×D2312yes—
288C22×C4#6726212yes—
289C22×C4(C2×D23)⋊C411yescharacteristic
290C22×C4(C2×D23)⋊C411yescharacteristic
291C22×C4(C2×D23)⋊C411yescharacteristic
292C22×C4C2×C4×D2311yescharacteristic
293C22×C4C2×D9211yescharacteristic
294C22×C4C2×C22⋊D2311yescharacteristic
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—922no—
299C2×C8—922no—
300C2×C8—922no—
301C4⋊C4—232no—
302C4⋊C4—461no—
303C4⋊C4—921no—
304C4⋊C4—921no—
305C4⋊C4—922no—
306C22⋊C4—464no—
307C22⋊C4—922no—
308C22⋊C4—922no—
309C22⋊C4—922no—
310C22⋊C4—921no—
311C22⋊C4—921no—
312C42—22no—
313C42—22no—
314C42—41no—
315C42—41no—
316C42—922no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—462no—
324C23—921no—
325C23—921no—
326C23—921no—
327C23—921no—
328C23—921no—
329C23—921no—
330C23(C2×D23)⋊C812yes—
331C23C2×(C2×D23)⋊C411yescharacteristic
332D4—922no—
333D4—922no—
334D4—928no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—462no—
354C2×C4—921no—
355C2×C4—921no—
356C2×C4—921no—
357C2×C4—921no—
358C2×C4—921no—
359C2×C4—921no—
360C2×C4—921no—
361C2×C4—921no—
362C2×C4—1844no—
363C2×C4#1062498812yes—
364C2×C4(C2×D23)⋊C812yes—
365C2×C4C2×C8×D2311yescharacteristic
366C2×C4C2×#6726211yescharacteristic
367C2×C4#1062507912yes—
368C2×C4#1062510311yescharacteristic
369C2×C4#1062511311yescharacteristic
370C8—82no—
371C8—1842no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—922no—
380C22—922no—
381C22—922no—
382C22—1841no—
383C22—1841no—
384C22—1841no—
385C22—1841no—
386C22C2×(C2×D23)⋊C811yescharacteristic
387C22C2×#1062498811yescharacteristic
388C22#1309239911yescharacteristic
389C22#1309241611yescharacteristic
390C22#1309242311yescharacteristic
391C22#1309243311yescharacteristic
392C22#1309243511yescharacteristic
393C4—22no—
394C4—22no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—22no—
400C4—41no—
401C4—922no—
402C4—1841no—
403C4—1841no—
404C2—42no—
405C2—1842no—
406C2#1567171311yescharacteristic
407C2#1567178211yescharacteristic
408C2#1567178911yescharacteristic
409C2#1567192711yescharacteristic
410C2#1567193811yescharacteristic
411C2#1567202911yescharacteristic
412C2#1567211711yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1797C2
socleC23×C23C2×C22⋊C4
hypercenter#1797D23
hypocenterC23#7599
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #15673465C2semidirect
3. #15671219C2semidirect
4. #15671217C2semidirect
5. C23×#1797C2semidirect
37. #10625101C8semidirect
168. #1797D23semidirect
262. C23#7599semidirect