Finite Group Databasebeta

← #19212146

Subgroups — #19212146

Order 5888.

538 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15675861C211yesmaximal, characteristic
2#15673143C211yesmaximal, characteristic, complemented
3#15671221C212yesmaximal, complemented
4#15671217C212yesmaximal
5C4×C23×C4⋊C8C211yesmaximal, characteristic, complemented
6C2×C4×D92C411yescharacteristic
7C2×#10625043—21no—
8C2×C4×C23⋊C8—21no—
9#13092319C411yescharacteristic
10#13092319C2211yescharacteristic
11#13092315C411yescharacteristic
12#13092315C2211yescharacteristic
13#13092308—21no—
14#13092308—21no—
15C4×C4⋊Dic23C411yescharacteristic
16C4×(C2×D23)⋊C4—21no—
17#13092172—21no—
18#13092172C2212yes—
19C2×C23×C4⋊C8—21no—
20C2×C4×C8×C23—21no—
21C43×C23C2211yescharacteristic
22C23×#336C2212yes—
23C22×D92C2×C411yescharacteristic
24C22×C4×D23—21no—
25C22×C8×C23—22no—
26C2×C42×C23C2×C411yescharacteristic
27C2×C42×C23C2×C411yescharacteristic
28C2×C42×C23D411yescharacteristic
29C2×C42×C23D411yescharacteristic
30C2×C42×C23D411yescharacteristic
31C2×C42×C23D411yescharacteristic
32C2×C42×C23C2311yescharacteristic
33C2×(C2×D23)⋊C4—21no—
34C2×(C2×D23)⋊C4—21no—
35C2×(C2×D23)⋊C4—21no—
36C2×(C2×D23)⋊C4—21no—
37C2×(C2×D23)⋊C4—21no—
38C2×C4⋊Dic23C2×C411yescharacteristic
39C2×C4⋊Dic23C2×C411yescharacteristic
40C2×C4⋊Dic23C2×C411yescharacteristic
41C2×Dic23⋊C4—21no—
42C2×Dic23⋊C4—21no—
43C2×C4×Dic23—21no—
44C22×C23⋊C8—22no—
45C4×D92—22no—
46C4×D92C814yescomplemented
47#10625043—42no—
48#10625043—42no—
49C23×C4⋊C8—24no—
50C4×C8×C23—42no—
51C23⋊#95—21no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C4×C23⋊C8—24no—
55C23×D23—21no—
56C22×C4×C23C22⋊C411yescharacteristic
57C22×C4×C23C22⋊C411yescharacteristic
58C22×C4×C23C22⋊C411yescharacteristic
59C22×C4×C23C22⋊C411yescharacteristic
60C22×C4×C23C22×C411yescharacteristic
61C22×C4×C23C2×D411yescharacteristic
62C22×C4×C23C2×D411yescharacteristic
63C22×Dic23—21no—
64C22×Dic23—21no—
65C22×Dic23—21no—
66C2×D92—21no—
67C2×D92—41no—
68C2×D92—41no—
69C2×D92C2×C812yes—
70C2×C4×D23—24no—
71C2×C4×D23—42no—
72C2×C4×D23—42no—
73C2×C8×C23—24no—
74C2×C8×C23—42no—
75C2×C8×C23—42no—
76C42×C23—22no—
77C42×C23—22no—
78C42×C23—22no—
79C42×C23—41no—
80C42×C23—41no—
81C42×C23C2×C812yes—
82C42×C23M1612yes—
83C42×C23D812yes—
84C42×C23SD1612yes—
85(C2×D23)⋊C4—24no—
86(C2×D23)⋊C4—42no—
87(C2×D23)⋊C4—42no—
88(C2×D23)⋊C4—41no—
89(C2×D23)⋊C4—41no—
90(C2×D23)⋊C4—42no—
91C4⋊Dic23—21no—
92C4⋊Dic23—41no—
93C4⋊Dic23—41no—
94C4⋊Dic23C2×C812yes—
95Dic23⋊C4—42no—
96Dic23⋊C4—41no—
97Dic23⋊C4—41no—
98C4×Dic23—42no—
99C2×C23⋊C8—24no—
100C2×C23⋊C8—42no—
101C2×C23⋊C8—42no—
102#7560—231nomaximal, Sylow
103C23×C23C2×C22⋊C411yescharacteristic
104C22×D23—22no—
105C22×D23—41no—
106C22×D23—41no—
107C22×D23—41no—
108C22×D23—41no—
109C22×D23—41no—
110C22×D23—41no—
111C2×C4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C22⋊C812yes—
124C2×C4×C23C22⋊C812yes—
125C2×C4×C23#10212yes—
126C2×C4×C23#10212yes—
127C2×C4×C23#10412yes—
128C2×C4×C23#10412yes—
129C2×C4×C23C22×C811yescharacteristic
130C2×C4×C23C2×M1611yescharacteristic
131C2×C4×C23C2×D811yescharacteristic
132C2×C4×C23C2×SD1611yescharacteristic
133C2×C4×C23#13512yes—
134C2×Dic23—22no—
135C2×Dic23—41no—
136C2×Dic23—41no—
137C2×Dic23—41no—
138C2×Dic23—41no—
139C2×Dic23—41no—
140C2×Dic23—41no—
141C2×Dic23—41no—
142C2×Dic23—41no—
143D92—42no—
144D92—42no—
145C4×D23—48no—
146C8×C23—44no—
147C23⋊C8—44no—
148#2293—231no—
149C4×C4⋊C8D2311yescharacteristic, complemented
150#1744—231no—
151#1271—232no—
152#1270—232no—
153C22×C23C2×C22⋊C811yescharacteristic
154C22×C23#41011yescharacteristic
155C22×C23#41311yescharacteristic
156C22×C23C2×#10211yescharacteristic
157C22×C23#41611yescharacteristic
158C22×C23C2×#10411yescharacteristic
159C22×C23C2×#10411yescharacteristic
160C2×D23—42no—
161C2×D23—42no—
162C2×D23—42no—
163C2×D23—81no—
164C2×D23—81no—
165C2×D23—81no—
166C2×D23—81no—
167C4×C23—22no—
168C4×C23—21no—
169C4×C23—21no—
170C4×C23—22no—
171C4×C23—22no—
172C4×C23—21no—
173C4×C23—21no—
174C4×C23—22no—
175C4×C23D4⋊C814yes—
176Dic23—42no—
177Dic23—81no—
178Dic23—81no—
179C2×C4×D4—231no—
180C2×#117—461no—
181C2×C4⋊C8—21no—
182C2×C4×C8—21no—
183C2×C4×C8—461no—
184#390—231no—
185#390—231no—
186#389—231no—
187#389—231no—
188#388—461no—
189#388—461no—
190C4×C4⋊C4—231no—
191C4×C22⋊C4—461no—
192C43C2×D2311yescharacteristic
193#336—232no—
194#336—461no—
195#336C2×D2312yes—
196C2×C23#145811yescharacteristic
197C2×C23C2×D4⋊C811yescharacteristic
198C2×C23#147611yescharacteristic
199C2×C23#150011yescharacteristic
200C2×C23#150211yescharacteristic
201C2×C23#152411yescharacteristic
202C2×C23#154011yescharacteristic
203D23—82no—
204C22×D4—231no—
205C23×C4—461no—
206C22×C8—22no—
207C22×C8—462no—
208C4×D4—234no—
209C4×D4—462no—
210#117—922no—
211#117—922no—
212C2×C4⋊C4—231no—
213C2×C4⋊C4—231no—
214C2×C4⋊C4—231no—
215C2×C4⋊C4—461no—
216C2×C4⋊C4—461no—
217C2×C22⋊C4—461no—
218C2×C22⋊C4—461no—
219C2×C22⋊C4—461no—
220C2×C22⋊C4—461no—
221C2×C22⋊C4—461no—
222C2×C42—461no—
223C2×C42C4×D2311yescharacteristic
224C2×C42C4×D2311yescharacteristic
225C2×C42D9211yescharacteristic
226C2×C42D9211yescharacteristic
227C2×C42C22⋊D2311yescharacteristic
228C2×C42C22⋊D2311yescharacteristic
229C2×C42C22×D2311yescharacteristic
230C4⋊C8—24no—
231C4×C8—42no—
232C4×C8—464no—
233#95—461no—
234#95—461no—
235#95—461no—
236C23#756011yescharacteristic, complemented, Sylow
237C24—461no—
238C2×D4—232no—
239C2×D4—461no—
240C2×D4—921no—
241C2×D4—921no—
242C22×C4—461no—
243C22×C4—464no—
244C22×C4—461no—
245C22×C4—461no—
246C22×C4—922no—
247C22×C4—922no—
248C22×C4(C2×D23)⋊C411yescharacteristic
249C22×C4(C2×D23)⋊C411yescharacteristic
250C22×C4(C2×D23)⋊C411yescharacteristic
251C22×C4(C2×D23)⋊C411yescharacteristic
252C22×C4C2×C4×D2311yescharacteristic
253C22×C4C2×D9211yescharacteristic
254C22×C4C2×C22⋊D2311yescharacteristic
255C2×C8—24no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—464no—
259C2×C8—922no—
260C2×C8—922no—
261C4⋊C4—232no—
262C4⋊C4—461no—
263C4⋊C4—921no—
264C4⋊C4—921no—
265C4⋊C4—921no—
266C4⋊C4—921no—
267C4⋊C4—922no—
268C22⋊C4—464no—
269C22⋊C4—922no—
270C22⋊C4—921no—
271C22⋊C4—921no—
272C22⋊C4—922no—
273C22⋊C4—922no—
274C42—22no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C42—922no—
280C42C8×D2312yes—
281C42#6726212yes—
282C42#6727212yes—
283C42#6727412yes—
284C23—462no—
285C23—921no—
286C23—921no—
287C23—921no—
288C23—921no—
289C23—921no—
290C23—921no—
291C23C2×(C2×D23)⋊C411yescharacteristic
292D4—922no—
293D4—922no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—462no—
307C2×C4—921no—
308C2×C4—921no—
309C2×C4—928no—
310C2×C4—921no—
311C2×C4—921no—
312C2×C4—921no—
313C2×C4—921no—
314C2×C4—921no—
315C2×C4—921no—
316C2×C4#1062498712yes—
317C2×C4#1062499112yes—
318C2×C4#1062499112yes—
319C2×C4(C2×D23)⋊C812yes—
320C2×C4(C2×D23)⋊C812yes—
321C2×C4#1062500712yes—
322C2×C4C2×C8×D2311yescharacteristic
323C2×C4C2×#6726211yescharacteristic
324C2×C4#1062507512yes—
325C2×C4C2×#6727211yescharacteristic
326C2×C4C2×#6727411yescharacteristic
327C8—44no—
328C8—924no—
329C22—922no—
330C22—922no—
331C22—922no—
332C22—1841no—
333C22—1841no—
334C22—1841no—
335C22—1841no—
336C22C2×(C2×D23)⋊C811yescharacteristic
337C22#1309239011yescharacteristic
338C22#1309239911yescharacteristic
339C22C2×#1062499111yescharacteristic
340C22#1309241411yescharacteristic
341C22C2×#1062500711yescharacteristic
342C22C2×#1062498711yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—22no—
350C4—22no—
351C4—922no—
352C4—1841no—
353C4—1841no—
354C4#1309214414yes—
355C2—1842no—
356C2#1567170911yescharacteristic
357C2C2×#1309214411yescharacteristic
358C2#1567178011yescharacteristic
359C2#1567188411yescharacteristic
360C2#1567189111yescharacteristic
361C2#1567198611yescharacteristic
362C2#1567204711yescharacteristic
subgroupG/H
centerC22×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC4×C23×C4⋊C8C2
socleC23×C23C2×C22⋊C4
hypercenterC4×C4⋊C8D23
hypocenterC23#7560
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #15673143C2semidirect
3. #15671221C2semidirect
5. C4×C23×C4⋊C8C2semidirect
46. C4×D92C8semidirect
149. C4×C4⋊C8D23semidirect
236. C23#7560semidirect