Finite Group Databasebeta

← #19212270

Subgroups — #19212270

Order 5888.

578 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675927C211yesmaximal, characteristic
2#15673376C211yesmaximal, characteristic
3D23×#336C211yesmaximal, characteristic
4#15671222C211yesmaximal, characteristic, complemented
5#15671222C211yesmaximal, characteristic, complemented
6#15671220C211yesmaximal, characteristic, complemented
7C23×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D23—21no—
9C2×#10625068C411yescharacteristic
10C2×#10625058C411yescharacteristic
11C2×C42×D23C2211yescharacteristic
12C2×Dic23⋊C8—21no—
13C2×(C2×D23)⋊C8—21no—
14#13092323C2211yescharacteristic
15#13092300—21no—
16#13092288—21no—
17#13092274C411yescharacteristic
18C4⋊C4×Dic23—21no—
19C4⋊C4×Dic23C411yescharacteristic
20#13092264—21no—
21#13092172C2211yescharacteristic
22#13092172C2211yescharacteristic
23#13092171—21no—
24C23×#389C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×C4×D23C2×C411yescharacteristic
28C22×C4×D23D411yescharacteristic
29C22×C4×D23D411yescharacteristic
30C22×Dic46C2×C411yescharacteristic
31C22×C8×C23—21no—
32C22×C8×C23—21no—
33C2×C4⋊C4×C23—21no—
34C2×C4⋊C4×C23C2×C411yescharacteristic
35C2×C4⋊C4×C23C2×C411yescharacteristic
36C2×C42×C23C2311yescharacteristic
37C2×(C2×D23)⋊C4—21no—
38C2×(C2×D23)⋊C4—21no—
39C2×C4⋊Dic23—21no—
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×C4×Dic23—21no—
43C2×C4×Dic23—21no—
44C2×C4×Dic23C2×C411yescharacteristic
45C2×C4×Dic23D411yescharacteristic
46C2×C4×Dic23D411yescharacteristic
47C22×C23⋊C8—21no—
48C22×C23⋊C8—21no—
49C2×C8×D23—24no—
50C2×C8×D23—42no—
51C2×C8×D23—42no—
52#10625068—22no—
53#10625068C814yescomplemented
54#10625058—42no—
55C42×D23—42no—
56C23×#95—21no—
57C23⋊#95—21no—
58C23⋊#95—21no—
59C23⋊#95—21no—
60C23⋊#95—21no—
61(C2×D23)⋊C8—42no—
62Dic23⋊C8—42no—
63C23×D23C22⋊C411yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23—21no—
66C22×C4×C23C22×C411yescharacteristic
67C22×C4×C23C2×D411yescharacteristic
68C22×C4×C23C2×D411yescharacteristic
69C22×Dic23—21no—
70C22×Dic23—21no—
71C22×Dic23C22⋊C411yescharacteristic
72C22×Dic23C22⋊C411yescharacteristic
73C22×Dic23C22⋊C411yescharacteristic
74C2×C4×D23—22no—
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C2×C4×D23—22no—
78C2×C4×D23—41no—
79C2×C4×D23—41no—
80C2×C4×D23—41no—
81C2×C4×D23—41no—
82C2×C4×D23C2×C812yes—
83C2×C4×D23M1612yes—
84C2×C4×D23SD1612yes—
85C2×C4×D23Q1612yes—
86C2×Dic46—21no—
87C2×Dic46—41no—
88C2×Dic46—41no—
89C2×Dic46C2×C812yescomplemented
90C2×C8×C23—22no—
91C2×C8×C23—41no—
92C2×C8×C23—41no—
93C2×C8×C23—41no—
94C2×C8×C23—41no—
95C2×C8×C23—41no—
96C4⋊C4×C23—21no—
97C4⋊C4×C23—41no—
98C4⋊C4×C23—41no—
99C4⋊C4×C23—41no—
100C4⋊C4×C23C2×C812yescomplemented
101C42×C23—41no—
102(C2×D23)⋊C4—24no—
103(C2×D23)⋊C4—42no—
104C4⋊Dic23—24no—
105C4⋊Dic23—41no—
106Dic23⋊C4—42no—
107C4×Dic23—22no—
108C4×Dic23—22no—
109C4×Dic23—41no—
110C4×Dic23—42no—
111C4×Dic23—42no—
112C2×C23⋊C8—22no—
113C2×C23⋊C8—41no—
114C2×C23⋊C8—41no—
115C2×C23⋊C8—41no—
116C2×C23⋊C8—41no—
117C2×C23⋊C8—41no—
118C8×D23—48no—
119#7589—231nomaximal, Sylow
120C23×C23C2×C22⋊C411yescharacteristic
121C22×D23—21no—
122C22×D23—21no—
123C22×D23—21no—
124C22×D23—21no—
125C22×D23C22⋊C812yes—
126C22×D23#10312yes—
127C22×D23#10412yes—
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—22no—
135C2×C4×C23—41no—
136C2×C4×C23—41no—
137C2×C4×C23—41no—
138C2×C4×C23—41no—
139C2×C4×C23—41no—
140C2×C4×C23C22×C811yescharacteristic
141C2×C4×C23C2×M1611yescharacteristic
142C2×C4×C23C2×SD1611yescharacteristic
143C2×C4×C23C2×Q1611yescharacteristic
144C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C23#13711yescharacteristic
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152C2×Dic23—22no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23—41no—
156C2×Dic23—41no—
157C2×Dic23—41no—
158C2×Dic23C22⋊C812yes—
159C2×Dic23#9912yes—
160C2×Dic23#10312yes—
161C4×D23—24no—
162C4×D23—24no—
163C4×D23—42no—
164C4×D23—42no—
165C4×D23—42no—
166C4×D23—42no—
167Dic46—42no—
168Dic46—42no—
169C8×C23—42no—
170C8×C23—81no—
171C23⋊C8—42no—
172C23⋊C8—81no—
173C4×C22⋊Q8—231no—
174#1797—231no—
175C2×#336—231no—
176#1272—231no—
177#1272—231no—
178#1271—231no—
179#1271D2311yescharacteristic, complemented
180C22×C23C2×C22⋊C811yescharacteristic
181C22×C23C2×#9911yescharacteristic
182C22×C23#41311yescharacteristic
183C22×C23C2×#10311yescharacteristic
184C22×C23#41711yescharacteristic
185C22×C23C2×#10411yescharacteristic
186C22×C23#42111yescharacteristic
187C2×D23—22no—
188C2×D23—22no—
189C2×D23—22no—
190C2×D23—22no—
191C2×D23—22no—
192C2×D23—22no—
193C2×D23Q8⋊C814yes—
194C4×C23—21no—
195C4×C23—21no—
196C4×C23—21no—
197C4×C23—21no—
198C4×C23—21no—
199C4×C23—21no—
200C4×C23—42no—
201C4×C23—81no—
202Dic23—22no—
203Dic23—22no—
204Dic23—22no—
205Dic23—42no—
206Dic23—81no—
207C23×C8—461no—
208C2×C22⋊Q8—231no—
209C2×C4×Q8—231no—
210C22×C42—231no—
211C2×C4⋊C8—461no—
212C2×C22⋊C8—461no—
213#391—231no—
214#389C2×D2311yescharacteristic
215#387—461no—
216#385—461no—
217#380—231no—
218C4×C4⋊C4—231no—
219C4×C4⋊C4—461no—
220C4×C22⋊C4—461no—
221#336—231no—
222#336—231no—
223#336—461no—
224#336C2×D2311yescharacteristic
225#336C2×D2311yescharacteristic
226C2×C23#145911yescharacteristic
227C2×C23C2×Q8⋊C811yescharacteristic
228C2×C23#147711yescharacteristic
229C2×C23#150411yescharacteristic
230C2×C23#152011yescharacteristic
231C2×C23#153211yescharacteristic
232C2×C23#155011yescharacteristic
233D23—24no—
234C22×Q8—231no—
235C23×C4—231no—
236C23×C4—231no—
237C23×C4—231no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—464no—
241C22×C8—461no—
242C22×C8—461no—
243C22×C8—922no—
244C22×C8—922no—
245C22⋊Q8—234no—
246C22⋊Q8—462no—
247C4×Q8—922no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—231no—
250C2×C4⋊C4—461no—
251C2×C4⋊C4—461no—
252C2×C4⋊C4C4×D2311yescharacteristic
253C2×C4⋊C4C4×D2311yescharacteristic
254C2×C22⋊C4—461no—
255C2×C22⋊C4—461no—
256C2×C42—231no—
257C2×C42—231no—
258C2×C42—231no—
259C2×C42—461no—
260C2×C42—461no—
261C2×C42—922no—
262C2×C42C22×D2311yescharacteristic
263C4⋊C8—922no—
264C22⋊C8—922no—
265#95—21no—
266#95—461no—
267#95—461no—
268#95—461no—
269#95—461no—
270C23#758911yescharacteristic, complemented, Sylow
271C24—231no—
272C2×Q8—232no—
273C2×Q8—461no—
274C2×Q8—921no—
275C2×Q8—921no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—231no—
279C22×C4—231no—
280C22×C4—231no—
281C22×C4—232no—
282C22×C4—232no—
283C22×C4—232no—
284C22×C4—232no—
285C22×C4—462no—
286C22×C4—462no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4—461no—
290C22×C4—461no—
291C22×C4—921no—
292C22×C4—921no—
293C22×C4—921no—
294C22×C4—921no—
295C22×C4C2×C4×D2311yescharacteristic
296C22×C4D4×D2311yescharacteristic
297C22×C4D4×D2311yescharacteristic
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—462no—
305C2×C8—928no—
306C2×C8—921no—
307C2×C8—921no—
308C2×C8—921no—
309C2×C8—921no—
310C2×C8—921no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—464no—
316C4⋊C4—921no—
317C4⋊C4—922no—
318C4⋊C4C8×D2312yescomplemented
319C22⋊C4—464no—
320C22⋊C4—922no—
321C42—41no—
322C42—462no—
323C42—462no—
324C42—921no—
325C42—922no—
326C42—922no—
327C23—232no—
328C23—232no—
329C23—232no—
330C23—461no—
331C23—461no—
332C23—461no—
333C23—461no—
334C23C22⋊C4×D2311yescharacteristic
335Q8—922no—
336Q8—922no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—232no—
350C2×C4—232no—
351C2×C4—232no—
352C2×C4—464no—
353C2×C4—464no—
354C2×C4—461no—
355C2×C4—461no—
356C2×C4—461no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—462no—
361C2×C4—922no—
362C2×C4—922no—
363C2×C4—922no—
364C2×C4—922no—
365C2×C4—921no—
366C2×C4—921no—
367C2×C4—921no—
368C2×C4—921no—
369C2×C4—921no—
370C2×C4C2×C8×D2311yescharacteristic
371C2×C4M16×D2311yescharacteristic
372C2×C4#1062508211yescharacteristic
373C2×C4SD16×D2311yescharacteristic
374C2×C4#1062508611yescharacteristic
375C2×C4Q16×D2311yescharacteristic
376C8—42no—
377C8—81no—
378C8—922no—
379C8—1841no—
380C22—234no—
381C22—462no—
382C22—462no—
383C22—462no—
384C22—462no—
385C22—462no—
386C22—462no—
387C22C22⋊C8×D2311yescharacteristic
388C22#99×D2311yescharacteristic
389C22#1309240011yescharacteristic
390C22#103×D2311yescharacteristic
391C22#1309241511yescharacteristic
392C22#104×D2311yescharacteristic
393C22#1309243211yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—81no—
402C4—462no—
403C4—462no—
404C4—462no—
405C4—922no—
406C4—1841no—
407C2—464no—
408C2#1567171411yescharacteristic
409C2D23×Q8⋊C811yescharacteristic
410C2#1567178111yescharacteristic
411C2#1567189811yescharacteristic
412C2#1567196711yescharacteristic
413C2#1567201611yescharacteristic
414C2#1567208611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7589
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. #15671222C2semidirect
5. #15671222C2semidirect
6. #15671220C2semidirect
7. C23×#1271C2semidirect
53. #10625068C8semidirect
89. C2×Dic46C2×C8semidirect
100. C4⋊C4×C23C2×C8semidirect
179. #1271D23semidirect
270. C23#7589semidirect
318. C4⋊C4C8×D23semidirect