Finite Group Databasebeta

← #19212202

Subgroups — #19212202

Order 5888.

668 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D23×#391C211yesmaximal, characteristic
2#15673376C211yesmaximal, characteristic
3#15673154C211yesmaximal, characteristic
4#15671223C211yesmaximal, characteristic, complemented
5#15671222C211yesmaximal, characteristic, complemented
6#15671222C211yesmaximal, characteristic, complemented
7C23×#1272C211yesmaximal, characteristic, complemented
8C22×Q8×D23C411yescharacteristic
9C2×C4⋊C4×D23C411yescharacteristic
10C2×C42×D23C2211yescharacteristic
11C2×Dic23⋊C8—21no—
12C2×(C2×D23)⋊C8—21no—
13C2×(C2×D23)⋊C8—21no—
14C2×C8×Dic23—21no—
15#13092324C411yescharacteristic
16#13092323C2211yescharacteristic
17#13092322C411yescharacteristic
18#13092321—21no—
19#13092321—21no—
20#95×D23—21no—
21#95×D23—21no—
22#13092172C2211yescharacteristic
23#13092172C2211yescharacteristic
24C23×#391C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×Q8×C23C2×C411yescharacteristic
28C2×Q8×D23—22no—
29C2×Q8×D23—42no—
30C2×Q8×D23—42no—
31C2×Q8×D23C814yescomplemented
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—
50C4⋊C4×D23—42no—
51C42×D23—42no—
52C23×#95—21no—
53C23×#95—21no—
54C23⋊#95—21no—
55C23⋊#95—21no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58C23⋊#95—21no—
59C23⋊#95—21no—
60(C2×D23)⋊C8—24no—
61(C2×D23)⋊C8—42no—
62Dic23⋊C8—42no—
63C8×Dic23—42no—
64C23×D23C22⋊C411yescharacteristic
65C2×Q8×C23—21no—
66C2×Q8×C23—41no—
67C2×Q8×C23—41no—
68C2×Q8×C23C2×C812yes—
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—24no—
84C2×C4×D23—22no—
85C2×C4×D23—21no—
86C2×C4×D23—21no—
87C2×C4×D23—41no—
88C2×C4×D23—41no—
89C2×C4×D23—41no—
90C2×C4×D23—42no—
91C2×C4×D23—42no—
92C2×C4×D23—42no—
93C2×C4×D23—42no—
94C2×C4×D23—42no—
95C2×C4×D23C2×C812yes—
96C2×C4×D23M1612yes—
97C2×C4×D23SD1612yes—
98C2×C4×D23Q1612yes—
99C2×Dic46—21no—
100C2×Dic46—24no—
101C2×Dic46—42no—
102C2×Dic46—42no—
103C2×Dic46—41no—
104C2×Dic46—41no—
105C2×Dic46C2×C812yes—
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—22no—
117C4×Dic23—22no—
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#7575—231nomaximal, Sylow
126C23×C23C2×C22⋊C411yescharacteristic
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—21no—
130C22×D23—21no—
131C22×D23C22⋊C812yes—
132C22×D23#10312yes—
133C22×D23#10412yes—
134Q8×C23—42no—
135Q8×C23—42no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—22no—
143C2×C4×C23—41no—
144C2×C4×C23—41no—
145C2×C4×C23—41no—
146C2×C4×C23—41no—
147C2×C4×C23—41no—
148C2×C4×C23C22×C811yescharacteristic
149C2×C4×C23C2×M1611yescharacteristic
150C2×C4×C23C2×SD1611yescharacteristic
151C2×C4×C23C2×Q1611yescharacteristic
152C2×C4×C23#13711yescharacteristic
153C2×C4×C23#13711yescharacteristic
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—22no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159C2×Dic23—21no—
160C2×Dic23—41no—
161C2×Dic23—41no—
162C2×Dic23—41no—
163C2×Dic23—41no—
164C2×Dic23—41no—
165C2×Dic23C22⋊C812yes—
166C2×Dic23#9912yes—
167C2×Dic23#10012yes—
168C2×Dic23#10312yes—
169C4×D23—24no—
170C4×D23—24no—
171C4×D23—42no—
172C4×D23—42no—
173C4×D23—42no—
174C4×D23—42no—
175C4×D23—48no—
176C4×D23—84no—
177Dic46—42no—
178Dic46—48no—
179Dic46—42no—
180C8×C23—42no—
181C8×C23—81no—
182C23⋊C8—42no—
183C23⋊C8—81no—
184C2×#391—231no—
185#1797—231no—
186C4×C22⋊C8—231no—
187#1272—231no—
188#1272—231no—
189#1272—231no—
190#1272D2311yescharacteristic, complemented
191C22×C23C2×C22⋊C811yescharacteristic
192C22×C23C2×#9911yescharacteristic
193C22×C23C2×#10011yescharacteristic
194C22×C23C2×#10311yescharacteristic
195C22×C23#41911yescharacteristic
196C22×C23C2×#10411yescharacteristic
197C22×C23#42111yescharacteristic
198C2×D23—22no—
199C2×D23—22no—
200C2×D23—22no—
201C2×D23—22no—
202C2×D23—22no—
203C2×D23—22no—
204C2×D23Q8⋊C814yes—
205C4×C23—21no—
206C4×C23—21no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—21no—
210C4×C23—21no—
211C4×C23—42no—
212C4×C23—81no—
213Dic23—22no—
214Dic23—42no—
215Dic23—41no—
216Dic23—81no—
217Dic23#32314yes—
218C23×Q8—231no—
219C22×C4⋊C4—231no—
220C22×C42—231no—
221C2×C4⋊C8—461no—
222C2×C22⋊C8—461no—
223C2×C22⋊C8—461no—
224C2×C4×C8—461no—
225#391—231no—
226#391—231no—
227#391—231no—
228#391—461no—
229#391—461no—
230#391C2×D2311yescharacteristic
231C2×#95—461no—
232C2×#95—461no—
233#336—231no—
234#336—231no—
235#336C2×D2311yescharacteristic
236#336C2×D2311yescharacteristic
237C2×C23C2×#32311yescharacteristic
238C2×C23C2×Q8⋊C811yescharacteristic
239C2×C23#147911yescharacteristic
240C2×C23#150811yescharacteristic
241C2×C23#152011yescharacteristic
242C2×C23#152711yescharacteristic
243C2×C23#154811yescharacteristic
244D23—24no—
245C22×Q8—234no—
246C22×Q8—231no—
247C22×Q8—461no—
248C22×Q8—462no—
249C22×Q8—922no—
250C22×Q8—922no—
251C22×Q8C4×D2311yescharacteristic
252C23×C4—231no—
253C23×C4—231no—
254C23×C4—231no—
255C23×C4—461no—
256C23×C4—461no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—461no—
260C22×C8—461no—
261C2×C4⋊C4—231no—
262C2×C4⋊C4—461no—
263C2×C4⋊C4—922no—
264C2×C4⋊C4C4×D2311yescharacteristic
265C2×C42—231no—
266C2×C42—231no—
267C2×C42—231no—
268C2×C42—922no—
269C2×C42C22×D2311yescharacteristic
270C4⋊C8—922no—
271C22⋊C8—464no—
272C22⋊C8—922no—
273C4×C8—922no—
274#95—21no—
275#95—21no—
276#95—461no—
277#95—461no—
278#95—461no—
279#95—461no—
280#95—461no—
281#95—461no—
282C23#757511yescharacteristic, complemented, Sylow
283C24—231no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—232no—
288C2×Q8—464no—
289C2×Q8—461no—
290C2×Q8—921no—
291C2×Q8—921no—
292C2×Q8—922no—
293C2×Q8—922no—
294C2×Q8—928no—
295C2×Q8—928no—
296C2×Q8C8×D2312yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—231no—
300C22×C4—231no—
301C22×C4—232no—
302C22×C4—232no—
303C22×C4—232no—
304C22×C4—232no—
305C22×C4—231no—
306C22×C4—462no—
307C22×C4—462no—
308C22×C4—462no—
309C22×C4—464no—
310C22×C4—461no—
311C22×C4—461no—
312C22×C4—461no—
313C22×C4—461no—
314C22×C4—921no—
315C22×C4—921no—
316C22×C4—921no—
317C22×C4—922no—
318C22×C4—922no—
319C22×C4—922no—
320C22×C4—922no—
321C22×C4—922no—
322C22×C4C2×C4×D2311yescharacteristic
323C22×C4D4×D2311yescharacteristic
324C22×C4D4×D2311yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—462no—
332C2×C8—921no—
333C2×C8—921no—
334C2×C8—921no—
335C2×C8—921no—
336C2×C8—921no—
337C4⋊C4—41no—
338C4⋊C4—921no—
339C4⋊C4—922no—
340C42—41no—
341C42—462no—
342C42—462no—
343C42—921no—
344C23—232no—
345C23—232no—
346C23—232no—
347C23—461no—
348C23—461no—
349C23—461no—
350C23—461no—
351C23C22⋊C4×D2311yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—922no—
355Q8—922no—
356Q8—928no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—232no—
370C2×C4—232no—
371C2×C4—232no—
372C2×C4—232no—
373C2×C4—464no—
374C2×C4—464no—
375C2×C4—461no—
376C2×C4—461no—
377C2×C4—462no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—461no—
381C2×C4—922no—
382C2×C4—922no—
383C2×C4—922no—
384C2×C4—922no—
385C2×C4—928no—
386C2×C4—921no—
387C2×C4—921no—
388C2×C4—921no—
389C2×C4—921no—
390C2×C4—921no—
391C2×C4—1844no—
392C2×C4C2×C8×D2311yescharacteristic
393C2×C4M16×D2311yescharacteristic
394C2×C4SD16×D2311yescharacteristic
395C2×C4#1062508611yescharacteristic
396C2×C4Q16×D2311yescharacteristic
397C2×C4#1062508911yescharacteristic
398C8—42no—
399C8—81no—
400C8—922no—
401C8—1841no—
402C22—234no—
403C22—462no—
404C22—462no—
405C22—462no—
406C22—462no—
407C22—462no—
408C22—462no—
409C22C22⋊C8×D2311yescharacteristic
410C22#99×D2311yescharacteristic
411C22#100×D2311yescharacteristic
412C22#103×D2311yescharacteristic
413C22#1309242411yescharacteristic
414C22#104×D2311yescharacteristic
415C22#1309243211yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4—234no—
425C4—462no—
426C4—921no—
427C4—922no—
428C4—1841no—
429C2—464no—
430C2D23×#32311yescharacteristic
431C2D23×Q8⋊C811yescharacteristic
432C2#1567179011yescharacteristic
433C2#1567191511yescharacteristic
434C2#1567196711yescharacteristic
435C2#1567199311yescharacteristic
436C2#1567207611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1272C2
socleC23×C23C2×C22⋊C4
hypercenter#1272D23
hypocenterC23#7575
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
4. #15671223C2semidirect
5. #15671222C2semidirect
6. #15671222C2semidirect
7. C23×#1272C2semidirect
31. C2×Q8×D23C8semidirect
190. #1272D23semidirect
282. C23#7575semidirect