Finite Group Databasebeta

← #19212339

Subgroups — #19212339

Order 5888.

612 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D23×#389C211yesmaximal, characteristic
2#15673464C211yesmaximal, characteristic
3#15673089C211yesmaximal, characteristic
4#15671221C211yesmaximal, characteristic, complemented
5#15671220C211yesmaximal, characteristic, complemented
6#15671219C211yesmaximal, characteristic, complemented
7C23×#1271C211yesmaximal, characteristic, complemented
8C22×#67262—21no—
9C2×C4⋊C4×D23—21no—
10C2×C4⋊C4×D23C411yescharacteristic
11C2×C4⋊C4×D23C411yescharacteristic
12C2×C42×D23C2211yescharacteristic
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—
50C2×#67262—24no—
51C2×#67262—42no—
52C2×#67262—42no—
53C4⋊C4×D23—22no—
54C4⋊C4×D23—22no—
55C4⋊C4×D23—42no—
56C4⋊C4×D23—42no—
57C4⋊C4×D23—42no—
58C42×D23—42no—
59C23×#95—21no—
60C23⋊#95—21no—
61C23⋊#95—21no—
62C23⋊#95—21no—
63(C2×D23)⋊C8—42no—
64C23×D23C22⋊C411yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C22×C4×C23C22×C411yescharacteristic
68C22×C4×C23C2×D411yescharacteristic
69C22×C4×C23C2×D411yescharacteristic
70C22×Dic23—21no—
71C22×Dic23—21no—
72C22×Dic23C22⋊C411yescharacteristic
73C22×Dic23C22⋊C411yescharacteristic
74C22×Dic23C22⋊C411yescharacteristic
75C2×C4×D23—22no—
76C2×C4×D23—22no—
77C2×C4×D23—22no—
78C2×C4×D23—21no—
79C2×C4×D23—21no—
80C2×C4×D23—22no—
81C2×C4×D23—24no—
82C2×C4×D23—22no—
83C2×C4×D23—21no—
84C2×C4×D23—21no—
85C2×C4×D23—41no—
86C2×C4×D23—42no—
87C2×C4×D23—42no—
88C2×C4×D23—42no—
89C2×C4×D23—42no—
90C2×C4×D23—42no—
91C2×C4×D23SD1612yes—
92C2×C4×D23Q1612yes—
93C2×C8×C23—22no—
94C2×C8×C23—41no—
95C2×C8×C23—41no—
96C2×C8×C23—41no—
97C2×C8×C23—41no—
98C2×C8×C23—41no—
99C4⋊C4×C23—21no—
100C4⋊C4×C23—41no—
101C4⋊C4×C23—41no—
102C4⋊C4×C23—41no—
103C4⋊C4×C23M1612yescomplemented
104C42×C23—41no—
105C4⋊Dic23—21no—
106C4⋊Dic23—42no—
107C4⋊Dic23—41no—
108C4⋊Dic23M1612yescomplemented
109Dic23⋊C4—24no—
110Dic23⋊C4—42no—
111Dic23⋊C4—42no—
112Dic23⋊C4—41no—
113Dic23⋊C4—41no—
114C4×Dic23—41no—
115C4×Dic23—41no—
116C4×Dic23—41no—
117C2×C23⋊C8—22no—
118C2×C23⋊C8—41no—
119C2×C23⋊C8—41no—
120C2×C23⋊C8—41no—
121C2×C23⋊C8—41no—
122C2×C23⋊C8—41no—
123#67262—48no—
124#7607—231nomaximal, Sylow
125C23×C23C2×C22⋊C411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—21no—
130C22×D23#9912yes—
131C22×D23#10312yes—
132C22×D23#10412yes—
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—22no—
140C2×C4×C23—41no—
141C2×C4×C23—41no—
142C2×C4×C23—41no—
143C2×C4×C23—41no—
144C2×C4×C23—41no—
145C2×C4×C23C2×M1611yescharacteristic
146C2×C4×C23C2×M1611yescharacteristic
147C2×C4×C23C2×SD1611yescharacteristic
148C2×C4×C23C2×Q1611yescharacteristic
149C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—22no—
156C2×Dic23—21no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159C2×Dic23—41no—
160C2×Dic23—41no—
161C2×Dic23—41no—
162C2×Dic23—41no—
163C2×Dic23—41no—
164C2×Dic23#10112yes—
165C2×Dic23#10312yes—
166C4×D23—24no—
167C4×D23—24no—
168C4×D23—24no—
169C4×D23—24no—
170C4×D23—42no—
171C4×D23—42no—
172C4×D23—48no—
173C4×D23—84no—
174C8×C23—42no—
175C8×C23—81no—
176C23⋊C8—42no—
177C23⋊C8—81no—
178C2×#389—231no—
179#1817—231no—
180#1728—231no—
181#1271—231no—
182#1271—231no—
183#1271—231no—
184#1271D2311yescharacteristic, complemented
185C22×C23#40711yescharacteristic
186C22×C23C2×#9911yescharacteristic
187C22×C23C2×#10111yescharacteristic
188C22×C23C2×#10311yescharacteristic
189C22×C23#41811yescharacteristic
190C22×C23C2×#10411yescharacteristic
191C22×C23#42111yescharacteristic
192C2×D23—22no—
193C2×D23—22no—
194C2×D23—22no—
195C2×D23—22no—
196C2×D23—22no—
197C2×D23—22no—
198C2×D23#32814yes—
199C4×C23—21no—
200C4×C23—21no—
201C4×C23—21no—
202C4×C23—21no—
203C4×C23—21no—
204C4×C23—21no—
205C4×C23—42no—
206C4×C23—81no—
207Dic23—22no—
208Dic23—22no—
209Dic23—42no—
210Dic23—41no—
211Dic23—81no—
212C22×M16—461no—
213C22×C4⋊C4—231no—
214C22×C4⋊C4—231no—
215C22×C4⋊C4—461no—
216C22×C42—231no—
217C2×C22⋊C8—461no—
218#389—231no—
219#389—231no—
220#389—231no—
221#389—461no—
222#389—461no—
223#389C2×D2311yescharacteristic
224C2×#95—461no—
225#336—231no—
226#336—231no—
227#336—461no—
228#336—461no—
229#336C2×D2311yescharacteristic
230#336C2×D2311yescharacteristic
231C2×C23#146311yescharacteristic
232C2×C23#148711yescharacteristic
233C2×C23#149011yescharacteristic
234C2×C23C2×#32811yescharacteristic
235C2×C23#151011yescharacteristic
236C2×C23#152811yescharacteristic
237C2×C23#154911yescharacteristic
238D23—24no—
239C23×C4—231no—
240C23×C4—231no—
241C23×C4—231no—
242C23×C4—461no—
243C23×C4—461no—
244C2×M16—464no—
245C2×M16—922no—
246C2×M16—922no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—461no—
250C22×C8—461no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—231no—
253C2×C4⋊C4—231no—
254C2×C4⋊C4—462no—
255C2×C4⋊C4—461no—
256C2×C4⋊C4—462no—
257C2×C4⋊C4—461no—
258C2×C4⋊C4—461no—
259C2×C4⋊C4—461no—
260C2×C4⋊C4—461no—
261C2×C4⋊C4—922no—
262C2×C4⋊C4—922no—
263C2×C4⋊C4—922no—
264C2×C4⋊C4C4×D2311yescharacteristic
265C2×C4⋊C4C4×D2311yescharacteristic
266C2×C42—231no—
267C2×C42—231no—
268C2×C42—231no—
269C2×C42—922no—
270C2×C42C22×D2311yescharacteristic
271C22⋊C8—922no—
272#95—21no—
273#95—461no—
274#95—461no—
275#95—461no—
276C23#760711yescharacteristic, complemented, Sylow
277C24—231no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—231no—
281C22×C4—231no—
282C22×C4—232no—
283C22×C4—232no—
284C22×C4—231no—
285C22×C4—462no—
286C22×C4—462no—
287C22×C4—462no—
288C22×C4—462no—
289C22×C4—462no—
290C22×C4—464no—
291C22×C4—461no—
292C22×C4—461no—
293C22×C4—461no—
294C22×C4—461no—
295C22×C4—461no—
296C22×C4—461no—
297C22×C4—921no—
298C22×C4—922no—
299C22×C4—922no—
300C22×C4—922no—
301C22×C4—922no—
302C22×C4—922no—
303C22×C4C2×C4×D2311yescharacteristic
304C22×C4D4×D2311yescharacteristic
305C22×C4D4×D2311yescharacteristic
306M16—928no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—462no—
314C2×C8—921no—
315C2×C8—921no—
316C2×C8—921no—
317C2×C8—921no—
318C2×C8—921no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—232no—
324C4⋊C4—464no—
325C4⋊C4—461no—
326C4⋊C4—921no—
327C4⋊C4—922no—
328C4⋊C4—922no—
329C4⋊C4—922no—
330C4⋊C4—921no—
331C4⋊C4—921no—
332C4⋊C4#6726212yescomplemented
333C42—41no—
334C42—921no—
335C42—921no—
336C42—921no—
337C23—232no—
338C23—232no—
339C23—232no—
340C23—461no—
341C23—461no—
342C23—461no—
343C23—461no—
344C23C22⋊C4×D2311yescharacteristic
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—232no—
358C2×C4—232no—
359C2×C4—464no—
360C2×C4—464no—
361C2×C4—464no—
362C2×C4—464no—
363C2×C4—461no—
364C2×C4—461no—
365C2×C4—461no—
366C2×C4—461no—
367C2×C4—462no—
368C2×C4—461no—
369C2×C4—461no—
370C2×C4—461no—
371C2×C4—922no—
372C2×C4—922no—
373C2×C4—928no—
374C2×C4—921no—
375C2×C4—921no—
376C2×C4—921no—
377C2×C4—921no—
378C2×C4—921no—
379C2×C4—1844no—
380C2×C4C2×#6726211yescharacteristic
381C2×C4M16×D2311yescharacteristic
382C2×C4#1062508211yescharacteristic
383C2×C4SD16×D2311yescharacteristic
384C2×C4#1062508511yescharacteristic
385C2×C4Q16×D2311yescharacteristic
386C8—42no—
387C8—81no—
388C8—922no—
389C8—1841no—
390C22—234no—
391C22—462no—
392C22—462no—
393C22—462no—
394C22—462no—
395C22—462no—
396C22—462no—
397C22#1309237911yescharacteristic
398C22#99×D2311yescharacteristic
399C22#101×D2311yescharacteristic
400C22#103×D2311yescharacteristic
401C22#1309242011yescharacteristic
402C22#104×D2311yescharacteristic
403C22#1309243211yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—42no—
411C4—81no—
412C4—462no—
413C4—462no—
414C4—922no—
415C4—921no—
416C4—1841no—
417C2—464no—
418C2#1567172511yescharacteristic
419C2#1567182411yescharacteristic
420C2#1567183811yescharacteristic
421C2D23×#32811yescharacteristic
422C2#1567192411yescharacteristic
423C2#1567199711yescharacteristic
424C2#1567208011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC22×C4×C23C22×C4
FrattiniC2×C42C22×D23
FittingC23×#1271C2
socleC23×C23C2×C22⋊C4
hypercenter#1271D23
hypocenterC23#7607
LCSG ▷ C22×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
103. C4⋊C4×C23M16semidirect
108. C4⋊Dic23M16semidirect
184. #1271D23semidirect
276. C23#7607semidirect
332. C4⋊C4#67262semidirect