Finite Group Databasebeta

← #19212284

Subgroups — #19212284

Order 5888.

566 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D23×#389C211yesmaximal, characteristic
2#15673464C211yesmaximal, characteristic
3#15673464C211yesmaximal, characteristic
4#15671221C211yesmaximal, characteristic, complemented
5#15671220C211yesmaximal, characteristic, complemented
6#15671219C211yesmaximal, characteristic, complemented
7C23×#1271C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D23—21no—
9C2×C4⋊C4×D23C411yescharacteristic
10C2×C4⋊C4×D23C411yescharacteristic
11C2×C42×D23C2211yescharacteristic
12C2×(C2×D23)⋊C8—21no—
13C2×(C2×D23)⋊C8—21no—
14#13092316C411yescharacteristic
15#13092315C2211yescharacteristic
16#13092314—21no—
17#13092313C411yescharacteristic
18#13092312—21no—
19#95×D23—21no—
20#13092172C2211yescharacteristic
21#13092172C2211yescharacteristic
22#13092171—21no—
23#13092171—21no—
24C23×#389C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×C4×D23—21no—
28C22×C4×D23—21no—
29C22×C4×D23C2×C411yescharacteristic
30C22×C4×D23D411yescharacteristic
31C22×C4×D23D411yescharacteristic
32C22×C8×C23—21no—
33C22×C8×C23—21no—
34C2×C4⋊C4×C23—21no—
35C2×C4⋊C4×C23C2×C411yescharacteristic
36C2×C4⋊C4×C23C2×C411yescharacteristic
37C2×C42×C23C2311yescharacteristic
38C2×C4⋊Dic23—21no—
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×Dic23⋊C4—21no—
44C2×Dic23⋊C4—21no—
45C2×C4×Dic23C2×C411yescharacteristic
46C2×C4×Dic23D411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C22×C23⋊C8—21no—
49C22×C23⋊C8—21no—
50C4⋊C4×D23—22no—
51C4⋊C4×D23—42no—
52C4⋊C4×D23—42no—
53C4⋊C4×D23—42no—
54C4⋊C4×D23C814yescomplemented
55C42×D23—42no—
56C23×#95—21no—
57C23⋊#95—21no—
58C23⋊#95—21no—
59C23⋊#95—21no—
60(C2×D23)⋊C8—42no—
61(C2×D23)⋊C8—42no—
62C23×D23C22⋊C411yescharacteristic
63C22×C4×C23—21no—
64C22×C4×C23—21no—
65C22×C4×C23C22×C411yescharacteristic
66C22×C4×C23C2×D411yescharacteristic
67C22×C4×C23C2×D411yescharacteristic
68C22×Dic23—21no—
69C22×Dic23—21no—
70C22×Dic23C22⋊C411yescharacteristic
71C22×Dic23C22⋊C411yescharacteristic
72C22×Dic23C22⋊C411yescharacteristic
73C2×C4×D23—22no—
74C2×C4×D23—22no—
75C2×C4×D23—24no—
76C2×C4×D23—22no—
77C2×C4×D23—22no—
78C2×C4×D23—21no—
79C2×C4×D23—21no—
80C2×C4×D23—21no—
81C2×C4×D23—21no—
82C2×C4×D23—41no—
83C2×C4×D23—41no—
84C2×C4×D23—42no—
85C2×C4×D23—42no—
86C2×C4×D23—42no—
87C2×C4×D23—42no—
88C2×C4×D23—42no—
89C2×C4×D23C2×C812yes—
90C2×C4×D23M1612yes—
91C2×C8×C23—41no—
92C2×C8×C23—41no—
93C2×C8×C23—41no—
94C2×C8×C23—41no—
95C2×C8×C23—41no—
96C2×C8×C23—41no—
97C4⋊C4×C23—21no—
98C4⋊C4×C23—41no—
99C4⋊C4×C23—41no—
100C4⋊C4×C23—41no—
101C4⋊C4×C23C2×C812yes—
102C42×C23—41no—
103C4⋊Dic23—21no—
104C4⋊Dic23—42no—
105C4⋊Dic23—41no—
106C4⋊Dic23C2×C812yes—
107Dic23⋊C4—24no—
108Dic23⋊C4—42no—
109Dic23⋊C4—42no—
110Dic23⋊C4—41no—
111Dic23⋊C4—41no—
112C4×Dic23—41no—
113C4×Dic23—41no—
114C4×Dic23—41no—
115C2×C23⋊C8—41no—
116C2×C23⋊C8—41no—
117C2×C23⋊C8—41no—
118C2×C23⋊C8—41no—
119C2×C23⋊C8—41no—
120C2×C23⋊C8—41no—
121#7593—231nomaximal, Sylow
122C23×C23C2×C22⋊C411yescharacteristic
123C22×D23—21no—
124C22×D23—21no—
125C22×D23—21no—
126C22×D23—21no—
127C22×D23C22⋊C812yes—
128C22×D23#9912yes—
129C22×D23#10112yes—
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—22no—
137C2×C4×C23—41no—
138C2×C4×C23—41no—
139C2×C4×C23—41no—
140C2×C4×C23—41no—
141C2×C4×C23—41no—
142C2×C4×C23C22×C811yescharacteristic
143C2×C4×C23C2×M1611yescharacteristic
144C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C23#13711yescharacteristic
147C2×C4×C23#13711yescharacteristic
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—22no—
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—21no—
157C2×Dic23—41no—
158C2×Dic23—41no—
159C2×Dic23—41no—
160C2×Dic23—41no—
161C2×Dic23—41no—
162C2×Dic23C22⋊C812yes—
163C4×D23—24no—
164C4×D23—24no—
165C4×D23—42no—
166C4×D23—42no—
167C4×D23—42no—
168C4×D23—42no—
169C4×D23—48no—
170C4×D23—84no—
171C8×C23—81no—
172C8×C23—81no—
173C23⋊C8—81no—
174C23⋊C8—81no—
175C2×#389—231no—
176#1817—231no—
177#1817—231no—
178#1271—231no—
179#1271—231no—
180#1271—231no—
181#1271D2311yescharacteristic, complemented
182C22×C23C2×C22⋊C811yescharacteristic
183C22×C23C2×#9911yescharacteristic
184C22×C23C2×#10111yescharacteristic
185C22×C23#41811yescharacteristic
186C22×C23#41911yescharacteristic
187C22×C23#42111yescharacteristic
188C22×C23#42111yescharacteristic
189C2×D23—22no—
190C2×D23—22no—
191C2×D23—22no—
192C2×D23—22no—
193C2×D23—22no—
194C2×D23—22no—
195C2×D23#32414yes—
196C4×C23—21no—
197C4×C23—21no—
198C4×C23—21no—
199C4×C23—21no—
200C4×C23—21no—
201C4×C23—21no—
202C4×C23—42no—
203C4×C23—81no—
204Dic23—22no—
205Dic23—42no—
206Dic23—41no—
207Dic23—41no—
208Dic23—81no—
209C22×C4⋊C4—231no—
210C22×C4⋊C4—231no—
211C22×C4⋊C4—461no—
212C22×C42—231no—
213C2×C22⋊C8—461no—
214C2×C22⋊C8—461no—
215#389—231no—
216#389—231no—
217#389—231no—
218#389—461no—
219#389—461no—
220#389C2×D2311yescharacteristic
221C2×#95—461no—
222#336—231no—
223#336—231no—
224#336—461no—
225#336—461no—
226#336C2×D2311yescharacteristic
227#336C2×D2311yescharacteristic
228C2×C23C2×#32411yescharacteristic
229C2×C23#147811yescharacteristic
230C2×C23#147911yescharacteristic
231C2×C23#151011yescharacteristic
232C2×C23#151111yescharacteristic
233C2×C23#153411yescharacteristic
234C2×C23#155611yescharacteristic
235D23—24no—
236C23×C4—231no—
237C23×C4—231no—
238C23×C4—231no—
239C23×C4—461no—
240C23×C4—461no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—461no—
244C22×C8—461no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—231no—
247C2×C4⋊C4—234no—
248C2×C4⋊C4—231no—
249C2×C4⋊C4—462no—
250C2×C4⋊C4—461no—
251C2×C4⋊C4—461no—
252C2×C4⋊C4—461no—
253C2×C4⋊C4—461no—
254C2×C4⋊C4—461no—
255C2×C4⋊C4—922no—
256C2×C4⋊C4—922no—
257C2×C4⋊C4—922no—
258C2×C4⋊C4C4×D2311yescharacteristic
259C2×C4⋊C4C4×D2311yescharacteristic
260C2×C42—231no—
261C2×C42—231no—
262C2×C42—231no—
263C2×C42—922no—
264C2×C42C22×D2311yescharacteristic
265C22⋊C8—922no—
266C22⋊C8—922no—
267#95—21no—
268#95—461no—
269#95—461no—
270#95—461no—
271C23#759311yescharacteristic, complemented, Sylow
272C24—231no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—231no—
276C22×C4—232no—
277C22×C4—232no—
278C22×C4—231no—
279C22×C4—231no—
280C22×C4—462no—
281C22×C4—462no—
282C22×C4—462no—
283C22×C4—462no—
284C22×C4—464no—
285C22×C4—461no—
286C22×C4—461no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4—461no—
290C22×C4—461no—
291C22×C4—921no—
292C22×C4—921no—
293C22×C4—922no—
294C22×C4—922no—
295C22×C4—922no—
296C22×C4—922no—
297C22×C4—922no—
298C22×C4C2×C4×D2311yescharacteristic
299C22×C4D4×D2311yescharacteristic
300C22×C4D4×D2311yescharacteristic
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—921no—
308C2×C8—921no—
309C2×C8—921no—
310C2×C8—921no—
311C2×C8—921no—
312C2×C8—921no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—232no—
318C4⋊C4—464no—
319C4⋊C4—461no—
320C4⋊C4—921no—
321C4⋊C4—922no—
322C4⋊C4—922no—
323C4⋊C4—922no—
324C4⋊C4—921no—
325C4⋊C4—921no—
326C4⋊C4C8×D2312yes—
327C42—41no—
328C42—921no—
329C42—921no—
330C42—921no—
331C23—232no—
332C23—232no—
333C23—232no—
334C23—461no—
335C23—461no—
336C23—461no—
337C23—461no—
338C23C22⋊C4×D2311yescharacteristic
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—232no—
352C2×C4—464no—
353C2×C4—464no—
354C2×C4—461no—
355C2×C4—461no—
356C2×C4—462no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—461no—
361C2×C4—461no—
362C2×C4—461no—
363C2×C4—922no—
364C2×C4—922no—
365C2×C4—922no—
366C2×C4—922no—
367C2×C4—928no—
368C2×C4—921no—
369C2×C4—921no—
370C2×C4—921no—
371C2×C4—921no—
372C2×C4—921no—
373C2×C4—1844no—
374C2×C4C2×C8×D2311yescharacteristic
375C2×C4M16×D2311yescharacteristic
376C2×C4#1062508211yescharacteristic
377C2×C4#1062508511yescharacteristic
378C2×C4#1062508611yescharacteristic
379C2×C4#1062508911yescharacteristic
380C8—81no—
381C8—81no—
382C8—1841no—
383C8—1841no—
384C22—234no—
385C22—462no—
386C22—462no—
387C22—462no—
388C22—462no—
389C22—462no—
390C22—462no—
391C22C22⋊C8×D2311yescharacteristic
392C22#99×D2311yescharacteristic
393C22#101×D2311yescharacteristic
394C22#1309242011yescharacteristic
395C22#1309242411yescharacteristic
396C22#1309243211yescharacteristic
397C22#1309243211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—462no—
407C4—921no—
408C4—921no—
409C4—922no—
410C4—1841no—
411C2—464no—
412C2D23×#32411yescharacteristic
413C2#1567178611yescharacteristic
414C2#1567179011yescharacteristic
415C2#1567192411yescharacteristic
416C2#1567192811yescharacteristic
417C2#1567202211yescharacteristic
418C2#1567211211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7593
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
4. #15671221C2semidirect
5. #15671220C2semidirect
6. #15671219C2semidirect
7. C23×#1271C2semidirect
54. C4⋊C4×D23C8semidirect
181. #1271D23semidirect
271. C23#7593semidirect