Finite Group Databasebeta

← #25025746

Subgroups — #25025746

Order 11008.

1558 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19132844C214yesmaximal, complemented
2#19132836C212yesmaximal
3#19132832C214yesmaximal, complemented
4#19132827C212yesmaximal, complemented
5#19132822C212yesmaximal, complemented
6C2×C43×#390C211yesmaximal, characteristic
7C22×C22⋊Dic43C2212yes—
8C22×C22⋊Dic43C2214yes—
9C22×C22⋊Dic43C2212yes—
10C22×C4×Dic43C2212yes—
11C2×C43⋊#95C2214yes—
12C2×C43⋊#95C2214yes—
13C2×C43⋊#95C2212yes—
14C2×C43⋊#95C2212yes—
15C2×C43⋊#95C2214yes—
16C2×C43⋊#95C2212yes—
17C23×D4×C43C2211yescharacteristic
18C22×C4⋊C4×C43C2211yescharacteristic
19C22×C22⋊C4×C43C2214yes—
20C22×C42×C43C2211yescharacteristic
21C43×#390C418yescomplemented
22C23×Dic43C2314yes—
23C23×Dic43C2314yes—
24C2×C22⋊Dic43—28no—
25C2×C22⋊Dic43—28no—
26C2×C22⋊Dic43—42no—
27C2×C22⋊Dic43—44no—
28C2×C22⋊Dic43—44no—
29C2×C22⋊Dic43—42no—
30C2×C22⋊Dic43—44no—
31C2×C4×Dic43—44no—
32C2×C4×Dic43—42no—
33C43⋊#95—28no—
34C43⋊#95—28no—
35C43⋊#95—44no—
36C43⋊#95—42no—
37C43⋊#95—42no—
38C43⋊#95—42no—
39C25×C43C2312yes—
40C22×D4×C43—24no—
41C22×D4×C43—42no—
42C22×D4×C43—41no—
43C22×D4×C43—41no—
44C22×D4×C43C2×C414yes—
45C23×C4×C43C2312yes—
46C23×C4×C43C2312yes—
47C23×C4×C43C2311yescharacteristic
48C2×C4⋊C4×C43—41no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43C2×C414yes—
51C2×C22⋊C4×C43—44no—
52C2×C22⋊C4×C43—44no—
53C2×C22⋊C4×C43C2×C4116yes—
54C2×C42×C43—42no—
55C2×C42×C43C2×C414yes—
56C24×C43—24no—
57C24×C43—24no—
58C24×C43—24no—
59C24×C43—24no—
60C24×C43—24no—
61C24×C43—24no—
62C24×C43—22no—
63C24×C43—22no—
64C24×C43C22×C414yes—
65C24×C43C2411yescharacteristic
66C2×D4×C43—28no—
67C2×D4×C43—44no—
68C2×D4×C43—44no—
69C2×D4×C43—48no—
70C2×D4×C43—48no—
71C22×C4×C43—24no—
72C22×C4×C43—22no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—24no—
78C22×C4×C43—24no—
79C22×C4×C43—24no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43C22×C414yes—
83C22×C4×C43C22×C414yes—
84C22×C4×C43C22×C412yes—
85C22×C4×C43#4114yes—
86C22×Dic43—24no—
87C22×Dic43—24no—
88C22×Dic43—24no—
89C22×Dic43—24no—
90C22×Dic43—24no—
91C22×Dic43—24no—
92C22×Dic43—24no—
93C22×Dic43—24no—
94C22×Dic43—24no—
95C22×Dic43—24no—
96C22×Dic43—24no—
97C22×Dic43—24no—
98C22×Dic43—24no—
99C22×Dic43#4118yes—
100C4⋊C4×C43—44no—
101C22⋊C4×C43—416no—
102C42×C43—44no—
103C22⋊Dic43—48no—
104C22⋊Dic43—416no—
105C22⋊Dic43—48no—
106C4×Dic43—48no—
107C23×C43—24no—
108C23×C43—28no—
109C23×C43—28no—
110C23×C43—24no—
111C23×C43—24no—
112C23×C43—44no—
113C23×C43—44no—
114C23×C43—44no—
115C23×C43—44no—
116C23×C43—44no—
117C23×C43—44no—
118C23×C43—42no—
119C23×C43—42no—
120C23×C43—44no—
121C23×C43—44no—
122C23×C43—44no—
123C23×C43—44no—
124C23×C43—44no—
125C23×C43—42no—
126C23×C43—44no—
127C23×C43—42no—
128C23×C43C23×C411yescharacteristic
129C23×C43C2×#4114yes—
130C23×C43C2×#4112yes—
131C23×C43H(5,𝔽2)12yes—
132C23×C43H(5,𝔽2)11yescharacteristic
133C23×C43H(5,𝔽2)11yescharacteristic
134C23×C43H(5,𝔽2)14yes—
135D4×C43—416no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—24no—
139C2×C4×C43—24no—
140C2×C4×C43—24no—
141C2×C4×C43—24no—
142C2×C4×C43—24no—
143C2×C4×C43—28no—
144C2×C4×C43—24no—
145C2×C4×C43—44no—
146C2×C4×C43—44no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—44no—
150C2×C4×C43#11714yes—
151C2×Dic43—28no—
152C2×Dic43—28no—
153C2×Dic43—28no—
154C2×Dic43—44no—
155C2×Dic43—44no—
156C2×Dic43—44no—
157C2×Dic43—44no—
158C2×Dic43—44no—
159C2×Dic43—44no—
160C2×Dic43—44no—
161C2×Dic43—44no—
162C2×Dic43—44no—
163C2×Dic43—44no—
164C2×Dic43—44no—
165#14503—431nomaximal, Sylow
166C22×C43—44no—
167C22×C43—48no—
168C22×C43—48no—
169C22×C43—44no—
170C22×C43—44no—
171C22×C43—84no—
172C22×C43—84no—
173C22×C43—84no—
174C22×C43—84no—
175C22×C43C2×#11711yescharacteristic
176C22×C43C4×#4112yes—
177C22×C43#51811yescharacteristic
178C22×C43#51811yescharacteristic
179C22×C43#51812yes—
180C22×C43#53814yes—
181C22×C43#53812yes—
182C22×C43#53812yes—
183C22×C43#54014yes—
184C22×C43#55112yes—
185C22×C43#55314yes—
186C22×C43#55512yes—
187C22×C43#55914yes—
188C22×C43#56012yes—
189C22×C43#56012yes—
190C4×C43—24no—
191C4×C43—44no—
192C4×C43—44no—
193Dic43—48no—
194Dic43—84no—
195C2×#390D4311yescharacteristic
196#1440—434no—
197#1438—432no—
198#1437—434no—
199#1436—432no—
200#1434—432no—
201C2×C43—84no—
202C2×C43#231211yescharacteristic
203C2×C43#233312yes—
204C2×C43#235712yes—
205C2×C43#237211yescharacteristic
206C2×C43#238011yescharacteristic
207C2×C43#279714yes—
208C2×C43#280314yes—
209C23×D4C2×D4311yescharacteristic
210C22×C4⋊C4C2×D4311yescharacteristic
211C22×C22⋊C4—432no—
212C22×C22⋊C4—434no—
213C22×C22⋊C4—432no—
214C22×C22⋊C4C2×D4314yes—
215C22×C42—432no—
216C22×C42C2×D4311yescharacteristic
217#390Dic4318yescomplemented
218C2×#95—434no—
219C2×#95—434no—
220C2×#95—432no—
221C2×#95—432no—
222C2×#95—434no—
223C2×#95—432no—
224C43#1450311yescharacteristic, complemented, Sylow
225C25C22×D4312yes—
226C22×D4—24no—
227C22×D4—42no—
228C22×D4—41no—
229C22×D4—41no—
230C22×D4C2×Dic4314yes—
231C23×C4—434no—
232C23×C4—434no—
233C23×C4C22×D4312yes—
234C23×C4C22×D4312yes—
235C23×C4C22×D4311yescharacteristic
236C2×C4⋊C4—41no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4C2×Dic4314yes—
239C2×C22⋊C4—44no—
240C2×C22⋊C4—44no—
241C2×C22⋊C4—868no—
242C2×C22⋊C4—868no—
243C2×C22⋊C4—1722no—
244C2×C22⋊C4—1724no—
245C2×C22⋊C4—1724no—
246C2×C22⋊C4—1722no—
247C2×C22⋊C4—1724no—
248C2×C22⋊C4C2×Dic43116yes—
249C2×C42—42no—
250C2×C42—1724no—
251C2×C42—1722no—
252C2×C42C2×Dic4314yes—
253#95—868no—
254#95—868no—
255#95—1722no—
256#95—1722no—
257#95—1724no—
258#95—1722no—
259C24—24no—
260C24—24no—
261C24—24no—
262C24—24no—
263C24—24no—
264C24—22no—
265C24—22no—
266C24—24no—
267C24C22×Dic4314yes—
268C24C23×D4311yescharacteristic
269C2×D4—28no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—48no—
273C2×D4—48no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—438no—
286C22×C4—864no—
287C22×C4—864no—
288C22×C4—864no—
289C22×C4—864no—
290C22×C4—864no—
291C22×C4—864no—
292C22×C4—864no—
293C22×C4—864no—
294C22×C4—864no—
295C22×C4—864no—
296C22×C4—864no—
297C22×C4—864no—
298C22×C4—864no—
299C22×C4#1062189814yes—
300C22×C4C22×Dic4314yes—
301C22×C4C22×Dic4314yes—
302C22×C4C22×Dic4312yes—
303C4⋊C4—44no—
304C22⋊C4—416no—
305C22⋊C4—1728no—
306C22⋊C4—17216no—
307C22⋊C4—1728no—
308C42—44no—
309C42—1728no—
310C23—24no—
311C23—28no—
312C23—28no—
313C23—24no—
314C23—24no—
315C23—42no—
316C23—42no—
317C23—44no—
318C23—44no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—42no—
323C23—44no—
324C23—42no—
325C23—44no—
326C23—44no—
327C23—44no—
328C23—44no—
329C23—44no—
330C23—44no—
331C23C23×Dic4311yescharacteristic
332C23#41×D4314yes—
333C23C2×#1062189812yes—
334C23#1306337011yescharacteristic
335C23#1306337014yes—
336C23#1306337011yescharacteristic
337C23#1306337012yes—
338D4—416no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—28no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—868no—
354C2×C4—868no—
355C2×C4—868no—
356C2×C4—1724no—
357C2×C4—1724no—
358C2×C4—1724no—
359C2×C4—1724no—
360C2×C4—1724no—
361C2×C4—1724no—
362C2×C4—1724no—
363C2×C4—1724no—
364C2×C4—1724no—
365C2×C4—1724no—
366C2×C4—1724no—
367C2×C4#1306328414yes—
368C22—48no—
369C22—48no—
370C22—44no—
371C22—44no—
372C22—44no—
373C22—84no—
374C22—84no—
375C22—84no—
376C22—84no—
377C22C2×#1306328411yescharacteristic
378C22#41×Dic4312yes—
379C22#1458337412yes—
380C22#1458337411yescharacteristic
381C22#1458337411yescharacteristic
382C22#1458348114yes—
383C22#1458348712yes—
384C22#1458348712yes—
385C22#1458349914yes—
386C22#1458357912yes—
387C22#1458359914yes—
388C22#1458361112yes—
389C22#1458363214yes—
390C22#1458363612yes—
391C22#1458363612yes—
392C4—24no—
393C4—44no—
394C4—44no—
395C4—3444no—
396C4—1728no—
397C2—84no—
398C2#1913719311yescharacteristic
399C2#1913736212yes—
400C2#1913756812yes—
401C2#1913770711yescharacteristic
402C2#1913777211yescharacteristic
403C2#1914244914yes—
404C2#1914252414yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#390C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#390D43
hypocenterC43#14503
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. #19132844C2semidirect
3. #19132832C2semidirect
4. #19132827C2semidirect
5. #19132822C2semidirect
21. C43×#390C4semidirect
217. #390Dic43semidirect
224. C43#14503semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191328442
#191328362
#191328322
#191328272
#191328222
C2×C43×#3902
#1450343