Finite Group Databasebeta

← #19212245

Subgroups — #19212245

Order 5888.

510 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675944C211yesmaximal, characteristic
2#15673539C211yesmaximal, characteristic, complemented
3#15673245C211yesmaximal, characteristic, complemented
4#15671222C211yesmaximal, characteristic, complemented
5#15671222C211yesmaximal, characteristic, complemented
6#15671218C211yesmaximal, characteristic
7C23×#1270C211yesmaximal, characteristic
8C2×#10625107C411yescharacteristic
9C2×#10625058C411yescharacteristic
10C2×D4×Dic23C411yescharacteristic
11C2×Dic23⋊C8—21no—
12C2×C8×Dic23—21no—
13#13092323C2211yescharacteristic
14#13092305—21no—
15#13092305—21no—
16#13092282C411yescharacteristic
17C22⋊C4×Dic23—21no—
18C22⋊C4×Dic23—21no—
19C42×Dic23C2211yescharacteristic
20#13092172C2211yescharacteristic
21#13092172C2211yescharacteristic
22#13092171—21no—
23#13092171—21no—
24C23×#390C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D4×C23C2×C411yescharacteristic
28C23×Dic23—21no—
29C22×Dic46C2×C411yescharacteristic
30C22×C8×C23—21no—
31C22×C8×C23—21no—
32C2×C4⋊C4×C23C2×C411yescharacteristic
33C2×C22⋊C4×C23—21no—
34C2×C22⋊C4×C23—21no—
35C2×C42×C23C2311yescharacteristic
36C2×C22⋊Dic23—21no—
37C2×C22⋊Dic23—21no—
38C2×C22⋊Dic23—21no—
39#10625107—22no—
40#10625107C814yescomplemented
41D4×Dic23—42no—
42C2×C4⋊Dic23C2×C411yescharacteristic
43C2×Dic23⋊C4—21no—
44C2×C4×Dic23—21no—
45C2×C4×Dic23C2×C411yescharacteristic
46C2×C4×Dic23C2×C411yescharacteristic
47C2×C4×Dic23D411yescharacteristic
48C2×C4×Dic23D411yescharacteristic
49C2×C4×Dic23D411yescharacteristic
50C2×C4×Dic23D411yescharacteristic
51C22×C23⋊C8—21no—
52C22×C23⋊C8—21no—
53#10625058—42no—
54C23⋊#95—21no—
55C23⋊#95—21no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58Dic23⋊C8—24no—
59C8×Dic23—42no—
60C24×C23—21no—
61C2×D4×C23—21no—
62C2×D4×C23—41no—
63C2×D4×C23—41no—
64C2×D4×C23C2×C812yes—
65C22×C4×C23—21no—
66C22×C4×C23C22×C411yescharacteristic
67C22×C4×C23C2×D411yescharacteristic
68C22×C4×C23C2×D411yescharacteristic
69C22×Dic23—21no—
70C22×Dic23—21no—
71C22×Dic23—42no—
72C22×Dic23—42no—
73C22×Dic23—42no—
74C22×Dic23C22⋊C411yescharacteristic
75C22×Dic23C22⋊C411yescharacteristic
76C22×Dic23C22⋊C411yescharacteristic
77C22×Dic23C22⋊C411yescharacteristic
78C2×Dic46—21no—
79C2×Dic46—41no—
80C2×Dic46—41no—
81C2×Dic46C2×C812yes—
82C2×C8×C23—22no—
83C2×C8×C23—41no—
84C2×C8×C23—41no—
85C2×C8×C23—41no—
86C2×C8×C23—41no—
87C2×C8×C23—41no—
88C4⋊C4×C23—41no—
89C22⋊C4×C23—41no—
90C22⋊C4×C23—41no—
91C22⋊C4×C23—41no—
92C22⋊C4×C23—41no—
93C42×C23—41no—
94C22⋊Dic23—24no—
95C22⋊Dic23—24no—
96C22⋊Dic23—42no—
97C4⋊Dic23—41no—
98Dic23⋊C4—42no—
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—22no—
104C4×Dic23—22no—
105C4×Dic23—41no—
106C4×Dic23—42no—
107C4×Dic23C2×C812yes—
108C4×Dic23M1612yes—
109C2×C23⋊C8—22no—
110C2×C23⋊C8—41no—
111C2×C23⋊C8—41no—
112C2×C23⋊C8—41no—
113C2×C23⋊C8—41no—
114C2×C23⋊C8—41no—
115#7584—231nomaximal, Sylow
116C23×C23—22no—
117C23×C23—41no—
118C23×C23—41no—
119C23×C23—41no—
120C23×C23—41no—
121C23×C23—41no—
122C23×C23—41no—
123C23×C23C2×C22⋊C411yescharacteristic
124D4×C23—42no—
125D4×C23—42no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—41no—
133C2×C4×C23—41no—
134C2×C4×C23—41no—
135C2×C4×C23C22×C811yescharacteristic
136C2×C4×C23C2×M1611yescharacteristic
137C2×C4×C23#13511yescharacteristic
138C2×C4×C23#13511yescharacteristic
139C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C23#13711yescharacteristic
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—22no—
150C2×Dic23—41no—
151C2×Dic23—41no—
152C2×Dic23—41no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23—84no—
156C2×Dic23C22⋊C812yes—
157C2×Dic23C22⋊C812yes—
158C2×Dic23#10012yes—
159C2×Dic23#10412yes—
160Dic46—42no—
161Dic46—42no—
162C8×C23—42no—
163C8×C23—81no—
164C23⋊C8—42no—
165C23⋊C8—81no—
166C4×#124—231no—
167#1839—231no—
168C4×C4⋊C8—231no—
169#1272—231no—
170#1272—231no—
171#1270—231no—
172#1270D2311yescharacteristic
173C22×C23—42no—
174C22×C23—42no—
175C22×C23—42no—
176C22×C23—81no—
177C22×C23—81no—
178C22×C23—81no—
179C22×C23—81no—
180C22×C23C2×C22⋊C811yescharacteristic
181C22×C23#41011yescharacteristic
182C22×C23C2×#10011yescharacteristic
183C22×C23#41611yescharacteristic
184C22×C23#41711yescharacteristic
185C22×C23C2×#10411yescharacteristic
186C22×C23#42111yescharacteristic
187C4×C23—21no—
188C4×C23—21no—
189C4×C23—21no—
190C4×C23—21no—
191C4×C23—21no—
192C4×C23—21no—
193C4×C23—81no—
194Dic23—22no—
195Dic23—22no—
196Dic23—22no—
197Dic23—22no—
198Dic23—42no—
199Dic23—81no—
200C2×#124—231no—
201C2×C4×Q8—231no—
202C2×C4×D4—231no—
203C2×C4⋊C8—461no—
204C2×C4×C8—461no—
205#391—231no—
206#390C2×D2311yescharacteristic
207#388—461no—
208#388—461no—
209#382—231no—
210C4×C22⋊C4—461no—
211C4×C22⋊C4—461no—
212C43—231no—
213#336—231no—
214#336—231no—
215#336—461no—
216#336—461no—
217#336C2×D2311yescharacteristic
218#336C2×D2311yescharacteristic
219C2×C23—82no—
220C2×C23#146011yescharacteristic
221C2×C23#147611yescharacteristic
222C2×C23#147711yescharacteristic
223C2×C23#150911yescharacteristic
224C2×C23#152111yescharacteristic
225C2×C23#152711yescharacteristic
226C2×C23#155111yescharacteristic
227C22×Q8—231no—
228C22×D4C4×D2311yescharacteristic
229C23×C4—461no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—461no—
233C22×C8—461no—
234#124—234no—
235#124—462no—
236C4×Q8—922no—
237C4×D4—922no—
238C2×C4⋊C4—231no—
239C2×C4⋊C4—461no—
240C2×C4⋊C4C4×D2311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—461no—
244C2×C22⋊C4—461no—
245C2×C22⋊C4—461no—
246C2×C42—231no—
247C2×C42—231no—
248C2×C42—231no—
249C2×C42—231no—
250C2×C42—231no—
251C2×C42—231no—
252C2×C42—461no—
253C2×C42C22×D2311yescharacteristic
254C4⋊C8—464no—
255C4×C8—922no—
256#95—461no—
257#95—461no—
258#95—461no—
259#95—461no—
260C23#758411yescharacteristic, complemented, Sylow
261C24—21no—
262C2×Q8—232no—
263C2×Q8—461no—
264C2×Q8—921no—
265C2×Q8—921no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4C8×D2312yes—
270C22×C4—21no—
271C22×C4—231no—
272C22×C4—231no—
273C22×C4—231no—
274C22×C4—231no—
275C22×C4—461no—
276C22×C4—461no—
277C22×C4—922no—
278C22×C4—922no—
279C22×C4—922no—
280C22×C4C2×C4×D2311yescharacteristic
281C22×C4D4×D2311yescharacteristic
282C22×C4D4×D2311yescharacteristic
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—462no—
290C2×C8—921no—
291C2×C8—921no—
292C2×C8—921no—
293C2×C8—921no—
294C2×C8—921no—
295C4⋊C4—41no—
296C4⋊C4—921no—
297C4⋊C4—922no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—464no—
303C22⋊C4—464no—
304C22⋊C4—922no—
305C42—41no—
306C42—232no—
307C42—232no—
308C42—462no—
309C42—462no—
310C42—461no—
311C42—461no—
312C42—461no—
313C42—461no—
314C42—921no—
315C42—922no—
316C23—22no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23C22⋊C4×D2311yescharacteristic
324Q8—922no—
325Q8—922no—
326D4—42no—
327D4—42no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—232no—
338C2×C4—232no—
339C2×C4—232no—
340C2×C4—232no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—461no—
344C2×C4—461no—
345C2×C4—461no—
346C2×C4—461no—
347C2×C4—461no—
348C2×C4—461no—
349C2×C4—462no—
350C2×C4—921no—
351C2×C4—921no—
352C2×C4—921no—
353C2×C4—921no—
354C2×C4—921no—
355C2×C4—1844no—
356C2×C4C2×C8×D2311yescharacteristic
357C2×C4M16×D2311yescharacteristic
358C2×C4#1062508211yescharacteristic
359C2×C4#1062508311yescharacteristic
360C2×C4#1062508611yescharacteristic
361C2×C4#1062508711yescharacteristic
362C8—42no—
363C8—81no—
364C8—922no—
365C8—1841no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22C22⋊C8×D2311yescharacteristic
374C22#1309238911yescharacteristic
375C22#100×D2311yescharacteristic
376C22#1309241011yescharacteristic
377C22#1309241511yescharacteristic
378C22#104×D2311yescharacteristic
379C22#1309243211yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—462no—
388C4—462no—
389C4—462no—
390C4—462no—
391C4—922no—
392C4—1841no—
393C2—82no—
394C2#1567171611yescharacteristic
395C2#1567177611yescharacteristic
396C2#1567178111yescharacteristic
397C2#1567191911yescharacteristic
398C2#1567197111yescharacteristic
399C2#1567199311yescharacteristic
400C2#1567208911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7584
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #15673539C2semidirect
3. #15673245C2semidirect
4. #15671222C2semidirect
5. #15671222C2semidirect
40. #10625107C8semidirect
260. C23#7584semidirect