Finite Group Databasebeta

← #19212348

Subgroups — #19212348

Order 5888.

676 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D23×#391C211yesmaximal, characteristic
2#15673464C211yesmaximal, characteristic
3#15673089C211yesmaximal, characteristic
4#15671223C211yesmaximal, characteristic, complemented
5#15671222C211yesmaximal, characteristic, complemented
6#15671222C211yesmaximal, characteristic, complemented
7C23×#1272C211yesmaximal, characteristic, complemented
8C22×Q8×D23C411yescharacteristic
9C22×#67262—21no—
10C2×C4⋊C4×D23C411yescharacteristic
11C2×C42×D23C2211yescharacteristic
12C2×(C2×D23)⋊C8—21no—
13#13092324C411yescharacteristic
14#13092323C2211yescharacteristic
15#13092322C411yescharacteristic
16#13092321—21no—
17#13092321—21no—
18#95×D23—21no—
19#95×D23—21no—
20#13092172C2211yescharacteristic
21#13092172C2211yescharacteristic
22#13092171—21no—
23#13092171—21no—
24C23×#391C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×Q8×C23C2×C411yescharacteristic
28C2×Q8×D23—22no—
29C2×Q8×D23—22no—
30C2×Q8×D23—42no—
31C2×Q8×D23—42no—
32C22×C4×D23—21no—
33C22×C4×D23—21no—
34C22×C4×D23C2×C411yescharacteristic
35C22×C4×D23D411yescharacteristic
36C22×C4×D23D411yescharacteristic
37C22×Dic46—21no—
38C22×Dic46C2×C411yescharacteristic
39C22×C8×C23—21no—
40C22×C8×C23—21no—
41C2×C4⋊C4×C23C2×C411yescharacteristic
42C2×C42×C23C2311yescharacteristic
43C2×C4⋊Dic23C2×C411yescharacteristic
44C2×Dic23⋊C4—21no—
45C2×C4×Dic23C2×C411yescharacteristic
46C2×C4×Dic23D411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C22×C23⋊C8—21no—
49C22×C23⋊C8—21no—
50C2×#67262—24no—
51C2×#67262—42no—
52C2×#67262—42no—
53C4⋊C4×D23—42no—
54C42×D23—42no—
55C23×#95—21no—
56C23×#95—21no—
57C23⋊#95—21no—
58C23⋊#95—21no—
59C23⋊#95—21no—
60C23⋊#95—21no—
61C23⋊#95—21no—
62C23⋊#95—21no—
63(C2×D23)⋊C8—42no—
64C23×D23C22⋊C411yescharacteristic
65C2×Q8×C23—21no—
66C2×Q8×C23—41no—
67C2×Q8×C23—41no—
68C2×Q8×C23M1612yescomplemented
69C22×C4×C23—21no—
70C22×C4×C23—21no—
71C22×C4×C23C22×C411yescharacteristic
72C22×C4×C23C2×D411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C22×Dic23—21no—
75C22×Dic23—21no—
76C22×Dic23C22⋊C411yescharacteristic
77C22×Dic23C22⋊C411yescharacteristic
78C22×Dic23C22⋊C411yescharacteristic
79Q8×D23—48no—
80Q8×D23—48no—
81C2×C4×D23—22no—
82C2×C4×D23—22no—
83C2×C4×D23—22no—
84C2×C4×D23—21no—
85C2×C4×D23—21no—
86C2×C4×D23—22no—
87C2×C4×D23—24no—
88C2×C4×D23—22no—
89C2×C4×D23—21no—
90C2×C4×D23—21no—
91C2×C4×D23—41no—
92C2×C4×D23—42no—
93C2×C4×D23—42no—
94C2×C4×D23—42no—
95C2×C4×D23—42no—
96C2×C4×D23—42no—
97C2×C4×D23SD1612yes—
98C2×C4×D23Q1612yes—
99C2×Dic46—24no—
100C2×Dic46—21no—
101C2×Dic46—42no—
102C2×Dic46—42no—
103C2×Dic46—41no—
104C2×Dic46—41no—
105C2×Dic46M1612yescomplemented
106C2×C8×C23—22no—
107C2×C8×C23—41no—
108C2×C8×C23—41no—
109C2×C8×C23—41no—
110C2×C8×C23—41no—
111C2×C8×C23—41no—
112C4⋊C4×C23—41no—
113C42×C23—41no—
114C4⋊Dic23—41no—
115Dic23⋊C4—42no—
116C4×Dic23—41no—
117C4×Dic23—41no—
118C4×Dic23—41no—
119C2×C23⋊C8—22no—
120C2×C23⋊C8—41no—
121C2×C23⋊C8—41no—
122C2×C23⋊C8—41no—
123C2×C23⋊C8—41no—
124C2×C23⋊C8—41no—
125#67262—48no—
126#7609—231nomaximal, Sylow
127C23×C23C2×C22⋊C411yescharacteristic
128C22×D23—21no—
129C22×D23—21no—
130C22×D23—21no—
131C22×D23—21no—
132C22×D23#9912yes—
133C22×D23#10312yes—
134C22×D23#10412yes—
135Q8×C23—42no—
136Q8×C23—42no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—22no—
144C2×C4×C23—41no—
145C2×C4×C23—41no—
146C2×C4×C23—41no—
147C2×C4×C23—41no—
148C2×C4×C23—41no—
149C2×C4×C23C2×M1611yescharacteristic
150C2×C4×C23C2×M1611yescharacteristic
151C2×C4×C23C2×SD1611yescharacteristic
152C2×C4×C23C2×Q1611yescharacteristic
153C2×C4×C23#13711yescharacteristic
154C2×C4×C23#13711yescharacteristic
155C2×Dic23—21no—
156C2×Dic23—21no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159C2×Dic23—22no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23—21no—
163C2×Dic23—41no—
164C2×Dic23—41no—
165C2×Dic23—41no—
166C2×Dic23—41no—
167C2×Dic23—41no—
168C2×Dic23#10012yes—
169C2×Dic23#10312yes—
170C4×D23—24no—
171C4×D23—24no—
172C4×D23—24no—
173C4×D23—24no—
174C4×D23—42no—
175C4×D23—42no—
176C4×D23—48no—
177C4×D23—84no—
178Dic46—48no—
179Dic46—42no—
180Dic46—42no—
181C8×C23—42no—
182C8×C23—81no—
183C23⋊C8—42no—
184C23⋊C8—81no—
185C2×#391—231no—
186#1817—231no—
187#1728—231no—
188#1272—231no—
189#1272—231no—
190#1272—231no—
191#1272D2311yescharacteristic, complemented
192C22×C23#40711yescharacteristic
193C22×C23C2×#9911yescharacteristic
194C22×C23C2×#10011yescharacteristic
195C22×C23C2×#10311yescharacteristic
196C22×C23#41911yescharacteristic
197C22×C23C2×#10411yescharacteristic
198C22×C23#42111yescharacteristic
199C2×D23—22no—
200C2×D23—22no—
201C2×D23—22no—
202C2×D23—22no—
203C2×D23—22no—
204C2×D23—22no—
205C2×D23#32814yes—
206C4×C23—21no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—21no—
210C4×C23—21no—
211C4×C23—21no—
212C4×C23—42no—
213C4×C23—81no—
214Dic23—22no—
215Dic23—22no—
216Dic23—42no—
217Dic23—41no—
218Dic23—81no—
219C23×Q8—231no—
220C22×M16—461no—
221C22×C4⋊C4—231no—
222C22×C42—231no—
223C2×C22⋊C8—461no—
224#391—231no—
225#391—231no—
226#391—231no—
227#391—461no—
228#391—461no—
229#391C2×D2311yescharacteristic
230C2×#95—461no—
231C2×#95—461no—
232#336—231no—
233#336—231no—
234#336—461no—
235#336—461no—
236#336C2×D2311yescharacteristic
237#336C2×D2311yescharacteristic
238C2×C23#146211yescharacteristic
239C2×C23#148711yescharacteristic
240C2×C23#149111yescharacteristic
241C2×C23C2×#32811yescharacteristic
242C2×C23#151111yescharacteristic
243C2×C23#152711yescharacteristic
244C2×C23#154811yescharacteristic
245D23—24no—
246C22×Q8—231no—
247C22×Q8—461no—
248C22×Q8—462no—
249C22×Q8—462no—
250C22×Q8—922no—
251C22×Q8—922no—
252C22×Q8C4×D2311yescharacteristic
253C23×C4—231no—
254C23×C4—231no—
255C23×C4—231no—
256C23×C4—461no—
257C23×C4—461no—
258C2×M16—464no—
259C2×M16—922no—
260C2×M16—922no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—461no—
264C22×C8—461no—
265C2×C4⋊C4—231no—
266C2×C4⋊C4—461no—
267C2×C4⋊C4—922no—
268C2×C4⋊C4C4×D2311yescharacteristic
269C2×C42—231no—
270C2×C42—231no—
271C2×C42—231no—
272C2×C42—922no—
273C2×C42C22×D2311yescharacteristic
274C22⋊C8—922no—
275#95—21no—
276#95—21no—
277#95—461no—
278#95—461no—
279#95—461no—
280#95—461no—
281#95—461no—
282#95—461no—
283C23#760911yescharacteristic, complemented, Sylow
284C24—231no—
285C2×Q8—21no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—232no—
289C2×Q8—464no—
290C2×Q8—461no—
291C2×Q8—921no—
292C2×Q8—921no—
293C2×Q8—922no—
294C2×Q8—922no—
295C2×Q8—928no—
296C2×Q8—928no—
297C2×Q8#6726212yescomplemented
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—231no—
301C22×C4—231no—
302C22×C4—232no—
303C22×C4—232no—
304C22×C4—231no—
305C22×C4—462no—
306C22×C4—462no—
307C22×C4—462no—
308C22×C4—462no—
309C22×C4—462no—
310C22×C4—464no—
311C22×C4—461no—
312C22×C4—461no—
313C22×C4—461no—
314C22×C4—461no—
315C22×C4—461no—
316C22×C4—461no—
317C22×C4—921no—
318C22×C4—922no—
319C22×C4—922no—
320C22×C4—922no—
321C22×C4—922no—
322C22×C4—922no—
323C22×C4C2×C4×D2311yescharacteristic
324C22×C4D4×D2311yescharacteristic
325C22×C4D4×D2311yescharacteristic
326M16—928no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—462no—
334C2×C8—921no—
335C2×C8—921no—
336C2×C8—921no—
337C2×C8—921no—
338C2×C8—921no—
339C4⋊C4—41no—
340C4⋊C4—921no—
341C4⋊C4—922no—
342C42—41no—
343C42—921no—
344C42—921no—
345C42—921no—
346C23—232no—
347C23—232no—
348C23—232no—
349C23—461no—
350C23—461no—
351C23—461no—
352C23—461no—
353C23C22⋊C4×D2311yescharacteristic
354Q8—42no—
355Q8—42no—
356Q8—922no—
357Q8—922no—
358Q8—928no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—232no—
372C2×C4—232no—
373C2×C4—464no—
374C2×C4—464no—
375C2×C4—464no—
376C2×C4—464no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—461no—
381C2×C4—462no—
382C2×C4—461no—
383C2×C4—461no—
384C2×C4—461no—
385C2×C4—922no—
386C2×C4—922no—
387C2×C4—928no—
388C2×C4—921no—
389C2×C4—921no—
390C2×C4—921no—
391C2×C4—921no—
392C2×C4—921no—
393C2×C4—1844no—
394C2×C4C2×#6726211yescharacteristic
395C2×C4M16×D2311yescharacteristic
396C2×C4SD16×D2311yescharacteristic
397C2×C4#1062508611yescharacteristic
398C2×C4Q16×D2311yescharacteristic
399C2×C4#1062508911yescharacteristic
400C8—42no—
401C8—81no—
402C8—922no—
403C8—1841no—
404C22—234no—
405C22—462no—
406C22—462no—
407C22—462no—
408C22—462no—
409C22—462no—
410C22—462no—
411C22#1309237911yescharacteristic
412C22#99×D2311yescharacteristic
413C22#100×D2311yescharacteristic
414C22#103×D2311yescharacteristic
415C22#1309242411yescharacteristic
416C22#104×D2311yescharacteristic
417C22#1309243211yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—462no—
427C4—462no—
428C4—921no—
429C4—922no—
430C4—1841no—
431C2—464no—
432C2#1567172211yescharacteristic
433C2#1567182411yescharacteristic
434C2#1567184211yescharacteristic
435C2D23×#32811yescharacteristic
436C2#1567192811yescharacteristic
437C2#1567199311yescharacteristic
438C2#1567207611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC22×C4×C23C22×C4
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7609
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #15671223C2semidirect
5. #15671222C2semidirect
6. #15671222C2semidirect
7. C23×#1272C2semidirect
68. C2×Q8×C23M16semidirect
105. C2×Dic46M16semidirect
191. #1272D23semidirect
283. C23#7609semidirect
297. C2×Q8#67262semidirect