Finite Group Databasebeta

← #25019303

Subgroups — #25019303

Order 11008.

2078 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063284C211yesmaximal, characteristic
2C22×C43⋊#95C211yesmaximal, characteristic
3#19132864C212yesmaximal, complemented
4#19132862C212yesmaximal, complemented
5#19132819C214yesmaximal, complemented
6#19132817C214yesmaximal
7C2×C43×#381C211yesmaximal, characteristic
8C24×Dic43C2212yes—
9C2×#13063284—24no—
10C2×#13063284—24no—
11C2×#13063284C418yescomplemented
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2212yes—
15C22×C4×Dic43C2212yes—
16C2×C43⋊#95—24no—
17C2×C43⋊#95C2218yes—
18C2×C43⋊#95C2212yes—
19C2×C43⋊#95C2212yes—
20C2×C43⋊#95C2218yes—
21C24×C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43C2212yes—
23C43×#381—24no—
24C2×#95×C43C2212yes—
25C2×#95×C43C2212yes—
26C23×Dic43—24no—
27C23×Dic43—28no—
28C23×Dic43—28no—
29C23×Dic43—44no—
30C23×Dic43C2312yes—
31C23×Dic43C2312yes—
32C23×Dic43C2314yes—
33#13063284—232no—
34C2×C4⋊Dic43—22no—
35C2×C4⋊Dic43—22no—
36C2×C4⋊Dic43—22no—
37C2×C4⋊Dic43—22no—
38C2×C4⋊Dic43C2×C414yescomplemented
39C2×C4⋊Dic43C2×C414yescomplemented
40C2×C22⋊Dic43—24no—
41C2×C22⋊Dic43—24no—
42C2×C22⋊Dic43C2×C418yes—
43C2×C4×Dic43—24no—
44C2×C4×Dic43—24no—
45C2×C4×Dic43C2×C418yescomplemented
46C43⋊#95—24no—
47C43⋊#95—24no—
48C43⋊#95—216no—
49C43⋊#95—48no—
50C25×C43C2311yescharacteristic
51C23×C4×C43—28no—
52C23×C4×C43C2×C414yes—
53C23×C4×C43D414yes—
54C23×C4×C43D414yes—
55C23×C4×C43C2314yes—
56C23×C4×C43C2311yescharacteristic
57C23×C4×C43C2311yescharacteristic
58C2×C22⋊C4×C43—24no—
59C2×C22⋊C4×C43—28no—
60#95×C43—24no—
61#95×C43—24no—
62C24×C43—24no—
63C24×C43—22no—
64C24×C43—22no—
65C24×C43C22×C412yes—
66C24×C43C2×D412yes—
67C24×C43C2×D412yes—
68C24×C43#4118yes—
69C24×C43C2411yescharacteristic
70C22×C4×C43—216no—
71C22×C4×C43—216no—
72C22×C4×C43—216no—
73C22×C4×C43—24no—
74C22×C4×C43—24no—
75C22×C4×C43—24no—
76C22×C4×C43—28no—
77C22×C4×C43—28no—
78C22×C4×C43—24no—
79C22×C4×C43—24no—
80C22×C4×C43C22⋊C4116yes—
81C22×C4×C43C22×C412yes—
82C22×C4×C43C22×C412yes—
83C22×C4×C43C2×D412yes—
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D412yes—
87C22×Dic43—216no—
88C22×Dic43—24no—
89C22×Dic43—22no—
90C22×Dic43—22no—
91C22×Dic43—22no—
92C22×Dic43—22no—
93C22×Dic43—28no—
94C22×Dic43—24no—
95C22×Dic43—28no—
96C22×Dic43—24no—
97C22×Dic43—28no—
98C22×Dic43—24no—
99C22×Dic43—432no—
100C22×Dic43—48no—
101C22×Dic43—48no—
102C22×Dic43C22×C414yes—
103C22×Dic43C22×C414yes—
104C22×Dic43#4118yes—
105C22⋊C4×C43—48no—
106C22⋊Dic43—216no—
107C4⋊Dic43—28no—
108C4⋊Dic43—28no—
109C4×Dic43—216no—
110C23×C43—24no—
111C23×C43—24no—
112C23×C43—24no—
113C23×C43—24no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—24no—
117C23×C43—216no—
118C23×C43—216no—
119C23×C43C2×C22⋊C414yes—
120C23×C43#11718yes—
121C23×C43#12318yes—
122C23×C43#12318yes—
123C23×C43C23×C411yescharacteristic
124C23×C43C22×D411yescharacteristic
125C23×C43C22×D411yescharacteristic
126C23×C43C2×#4114yes—
127C23×C43C2×#4114yes—
128C23×C43H(5,𝔽2)12yes—
129C23×C432−1+412yes—
130C2×C4×C43—24no—
131C2×C4×C43—24no—
132C2×C4×C43—24no—
133C2×C4×C43—24no—
134C2×C4×C43—24no—
135C2×C4×C43—24no—
136C2×C4×C43—232no—
137C2×C4×C43—44no—
138C2×C4×C43—44no—
139C2×C4×C43—44no—
140C2×C4×C43—48no—
141C2×C4×C43—48no—
142C2×C4×C43C2×C22⋊C414yes—
143C2×C4×C43C2×C22⋊C414yes—
144C2×Dic43—24no—
145C2×Dic43—24no—
146C2×Dic43—28no—
147C2×Dic43—28no—
148C2×Dic43—28no—
149C2×Dic43—216no—
150C2×Dic43—432no—
151C2×Dic43—44no—
152C2×Dic43—44no—
153C2×Dic43—44no—
154C2×Dic43—42no—
155C2×Dic43—44no—
156C2×Dic43—42no—
157C2×Dic43—44no—
158C2×Dic43—48no—
159#13958—431nomaximal, Sylow
160C22×C43—24no—
161C22×C43—216no—
162C22×C43—28no—
163C22×C43—28no—
164C22×C43—216no—
165C22×C43—24no—
166C22×C43#38118yes—
167C22×C43C22×C22⋊C411yescharacteristic
168C22×C43C2×#11712yes—
169C22×C43C4×#4112yes—
170C22×C43#52012yes—
171C22×C43C2×#12312yes—
172C22×C43C2×#12312yes—
173C22×C43#52512yes—
174C22×C43#53212yes—
175C22×C43#53511yescharacteristic
176C22×C43#53611yescharacteristic
177C22×C43#53712yes—
178C22×C43#55118yes—
179C22×C43#55218yes—
180C4×C43—24no—
181C4×C43—24no—
182C4×C43—84no—
183Dic43—44no—
184Dic43—48no—
185Dic43—44no—
186C22×#117—431no—
187C2×#381D4311yescharacteristic
188C22×#95—431no—
189#1445—432no—
190#1445—432no—
191#1434—434no—
192C22⋊#95—434no—
193C2×C43—28no—
194C2×C43C2×#38111yescharacteristic
195C2×C43#229711yescharacteristic
196C2×C43#231111yescharacteristic
197C2×C43#234314yes—
198C2×C43#248212yes—
199C2×C43#248412yes—
200C2×C43#249814yes—
201C24×C4—432no—
202C24×C4C2×D4311yescharacteristic
203C2×#117—438no—
204C2×#117—864no—
205C2×#117—864no—
206C22×C4⋊C4—431no—
207C22×C4⋊C4—431no—
208C22×C22⋊C4—432no—
209C22×C22⋊C4C2×D4312yes—
210C22×C42—432no—
211#381—24no—
212C2×#95—438no—
213C2×#95—432no—
214C2×#95—432no—
215C2×#95—438no—
216C2×#95—864no—
217C2×#95C2×D4312yes—
218C2×#95C2×D4312yes—
219C43#1395811yescharacteristic, complemented, Sylow
220C25C22×D4311yescharacteristic
221C23×C4—28no—
222C23×C4—432no—
223C23×C4—432no—
224C23×C4—434no—
225C23×C4—868no—
226C23×C4—864no—
227C23×C4—868no—
228C23×C4—1724no—
229C23×C4C4×D4314yes—
230C23×C4D17214yes—
231C23×C4C22⋊D4314yes—
232C23×C4C22×D4314yes—
233C23×C4C22×D4311yescharacteristic
234C23×C4C22×D4311yescharacteristic
235#117—8632no—
236C2×C4⋊C4—434no—
237C2×C4⋊C4—434no—
238C2×C4⋊C4—862no—
239C2×C4⋊C4—862no—
240C2×C4⋊C4—862no—
241C2×C4⋊C4—862no—
242C2×C22⋊C4—28no—
243C2×C22⋊C4—24no—
244C2×C22⋊C4—438no—
245C2×C22⋊C4—864no—
246C2×C22⋊C4—864no—
247C2×C42—438no—
248C2×C42—864no—
249C2×C42—864no—
250#95—24no—
251#95—24no—
252#95—8616no—
253#95—864no—
254#95—864no—
255#95—1728no—
256C24—24no—
257C24—22no—
258C24—22no—
259C24C2×C4×D4312yes—
260C24C2×D17212yes—
261C24#1062190018yes—
262C24C2×C22⋊D4312yes—
263C24C23×D4311yescharacteristic
264C22×C4—216no—
265C22×C4—216no—
266C22×C4—216no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—28no—
271C22×C4—28no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—434no—
275C22×C4—434no—
276C22×C4—438no—
277C22×C4—8616no—
278C22×C4—862no—
279C22×C4—862no—
280C22×C4—864no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4—868no—
284C22×C4—864no—
285C22×C4—868no—
286C22×C4—864no—
287C22×C4—868no—
288C22×C4—864no—
289C22×C4—17232no—
290C22×C4—1728no—
291C22×C4—1728no—
292C22×C4(C2×D43)⋊C4116yes—
293C22×C4C2×C4×D4312yes—
294C22×C4C2×C4×D4312yes—
295C22×C4C2×D17212yes—
296C22×C4C2×D17212yes—
297C22×C4C2×C22⋊D4312yes—
298C22×C4C2×C22⋊D4312yes—
299C4⋊C4—868no—
300C4⋊C4—868no—
301C22⋊C4—48no—
302C22⋊C4—8616no—
303C42—8616no—
304C23—216no—
305C23—216no—
306C23—24no—
307C23—24no—
308C23—24no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—24no—
313C23C2×(C2×D43)⋊C414yes—
314C23#1306328118yes—
315C23#1306330618yes—
316C23#1306330918yes—
317C23C22×C4×D4311yescharacteristic
318C23C22×C22⋊D4311yescharacteristic
319C23C22×D17211yescharacteristic
320C23#41×D4314yes—
321C23C2×#1062190014yes—
322C23#1306337112yes—
323C23#1306337212yes—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—232no—
331C2×C4—48no—
332C2×C4—48no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—8616no—
337C2×C4—864no—
338C2×C4—864no—
339C2×C4—868no—
340C2×C4—868no—
341C2×C4—868no—
342C2×C4—17232no—
343C2×C4—1728no—
344C2×C4—1724no—
345C2×C4—1724no—
346C2×C4—1724no—
347C2×C4—1724no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4—1724no—
351C2×C4C2×(C2×D43)⋊C414yes—
352C2×C4C2×(C2×D43)⋊C414yes—
353C22—28no—
354C22—24no—
355C22—28no—
356C22—24no—
357C22—216no—
358C22—216no—
359C22#1458276018yes—
360C22C22×(C2×D43)⋊C411yescharacteristic
361C22C2×#1306328112yes—
362C22#1458336712yes—
363C22#1458337912yes—
364C22C2×#1306330612yes—
365C22C2×#1306330912yes—
366C22#1458341112yes—
367C22#1458344512yes—
368C22#1458346811yescharacteristic
369C22#1458347511yescharacteristic
370C22#1458347712yes—
371C22#1458357218yes—
372C22#1458358618yes—
373C4—24no—
374C4—24no—
375C4—84no—
376C4—1728no—
377C4—1724no—
378C4—1724no—
379C2—28no—
380C2C2×#1458276011yescharacteristic
381C2#1913708311yescharacteristic
382C2#1913718311yescharacteristic
383C2#1913745714yes—
384C2#1913887112yes—
385C2#1913888412yes—
386C2#1913904114yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#381C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#381D43
hypocenterC43#13958
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #19132864C2semidirect
4. #19132862C2semidirect
5. #19132819C2semidirect
11. C2×#13063284C4semidirect
38. C2×C4⋊Dic43C2×C4semidirect
39. C2×C4⋊Dic43C2×C4semidirect
45. C2×C4×Dic43C2×C4semidirect
219. C43#13958semidirect

Maximal subgroups

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

subgroupindex
C22×#130632842
C22×C43⋊#952
#191328642
#191328622
#191328192
#191328172
C2×C43×#3812
#1395843