Finite Group Databasebeta

← #25098687

Subgroups — #25098687

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic43⋊C8C211yesmaximal, characteristic
2C2×#14582855C211yesmaximal, characteristic
3#19137077C211yesmaximal, characteristic
4#19135157C214yesmaximal, complemented
5#19135150C214yesmaximal, complemented
6#19134293C211yesmaximal, characteristic
7#19134291C211yesmaximal, characteristic
8#19134288C211yesmaximal, characteristic
9C43×#1729C211yesmaximal, characteristic
10C22×#10621877C2211yescharacteristic
11C23×C43⋊C8C2211yescharacteristic
12C2×#13063284C2211yescharacteristic
13C22×C4×Dic43C2211yescharacteristic
14C2×Dic43⋊C8—24no—
15C2×Dic43⋊C8C2212yes—
16C2×Dic43⋊C8C2212yes—
17#14582855—24no—
18C2×#13063236C2212yes—
19C2×C4×C43⋊C8C2212yes—
20#14582795C412yes—
21#14582795C412yes—
22#14582771C412yes—
23#14582771C412yes—
24C4×Dic43⋊C4C2214yes—
25#14582653C2214yes—
26#14582653C2214yes—
27#14582653C2212yes—
28#14582653C2212yes—
29C22×M16×C43C2211yescharacteristic
30C23×C8×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C43×#336C2214yes—
33C23×Dic43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C2×#10621877—22no—
36C2×#10621877—22no—
37C2×#10621877Q814yes—
38C22×C43⋊C8—22no—
39C22×C43⋊C8—22no—
40C22×C43⋊C8D414yes—
41C22×C43⋊C8C2311yescharacteristic
42C22×C43⋊C8C2311yescharacteristic
43C22×C43⋊C8C2312yes—
44#13063284—22no—
45#13063284—22no—
46C2×C4⋊Dic43C2×C412yes—
47C2×Dic43⋊C4C2×C414yes—
48C2×Dic43⋊C4C2×C414yes—
49C2×C22⋊Dic43C2×C412yes—
50C2×C4×Dic43—22no—
51C2×C4×Dic43—22no—
52C2×C4×Dic43C2×C412yes—
53C2×C4×Dic43C2312yes—
54C2×C4×Dic43C2312yes—
55Dic43⋊C8—24no—
56Dic43⋊C8—24no—
57#13063236—24no—
58C4×C43⋊C8—24no—
59C43⋊#95C2×C414yes—
60C43⋊#95C2×C414yes—
61C23×C4×C43C2311yescharacteristic
62C2×M16×C43—22no—
63C2×M16×C43—22no—
64C2×M16×C43—22no—
65C22×C8×C43—22no—
66C22×C8×C43—22no—
67C22×C8×C43—22no—
68C22×C8×C43C2312yes—
69C22×C8×C43C2312yes—
70#117×C43—22no—
71#117×C43—22no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C22⋊C4×C43C2×C412yes—
75C2×C42×C43C2312yes—
76C24×C43C22×C411yescharacteristic
77C22×C4×C43C22×C412yes—
78C22×C4×C43C22×C412yes—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D412yes—
81C22×C4×C43C2×Q812yes—
82C22×C4×C43#4112yes—
83C22×C4×C43#4112yes—
84C22×C4×C43#4112yes—
85C22×C4×C43#4112yes—
86C22×C4×C43C2411yescharacteristic
87C22×Dic43—24no—
88C22×Dic43—22no—
89C22×Dic43—22no—
90C22×Dic43—42no—
91C22×Dic43C22×C412yes—
92C22×Dic43C22×C414yes—
93C22×Dic43C22×C412yes—
94M16×C43—44no—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—44no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C22⋊C4×C43—24no—
105C42×C43—22no—
106C42×C43—22no—
107C22⋊Dic43—24no—
108C4⋊Dic43—24no—
109Dic43⋊C4—28no—
110Dic43⋊C4—44no—
111C4×Dic43—24no—
112C4×Dic43—22no—
113C4×Dic43—22no—
114C4×Dic43—22no—
115C4×Dic43—22no—
116#10621877—28no—
117C2×C43⋊C8—28no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8C2×D412yes—
125C2×C43⋊C8C2×D412yes—
126C2×C43⋊C8C2×Q814yes—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43#11712yes—
130C23×C43C4×D412yes—
131C23×C43C4×Q812yes—
132C23×C43C23×C411yescharacteristic
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—24no—
136C2×C4×C43—24no—
137C2×C4×C43#11712yes—
138C2×C4×C43C4×D412yes—
139C2×C4×C43C4×Q812yes—
140C2×C4×C43C22⋊Q814yes—
141C2×C4×C43#12314yes—
142C2×C4×C43#12514yes—
143C2×C4×C43#12614yes—
144C2×C4×C43C22×D411yescharacteristic
145C2×C4×C43C22×Q811yescharacteristic
146C2×C4×C43C2×#4111yescharacteristic
147C2×C4×C43C2×#4111yescharacteristic
148C2×C4×C43C2×#4111yescharacteristic
149C2×C4×C43C2×#4111yescharacteristic
150C2×Dic43—28no—
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—24no—
154C2×Dic43—22no—
155C2×Dic43—24no—
156C2×Dic43—22no—
157C2×Dic43—24no—
158C2×Dic43—22no—
159C2×Dic43—44no—
160C2×Dic43#13114yes—
161C8×C43—42no—
162C8×C43—42no—
163C43⋊C8—24no—
164C43⋊C8—22no—
165C43⋊C8—22no—
166#21024—431nomaximal, Sylow
167C22×C43—24no—
168C22×C43—22no—
169C22×C43—22no—
170C22×C43—24no—
171C22×C43#38714yes—
172C22×C43C2×#11711yescharacteristic
173C22×C43C2×C4×D411yescharacteristic
174C22×C43C2×C4×Q811yescharacteristic
175C22×C43C2×#13112yes—
176C22×C43#56812yes—
177C4×C43—42no—
178C4×C43—42no—
179C4×C43#38714yes—
180C4×C43C2×C22⋊Q811yescharacteristic
181C4×C43C2×#12311yescharacteristic
182C4×C43C2×#12511yescharacteristic
183C4×C43C2×#12611yescharacteristic
184Dic43—24no—
185Dic43—44no—
186Dic43—42no—
187C22×C4⋊C8—431no—
188C2×#405—431no—
189#2296—431no—
190#1917—434no—
191#1916—434no—
192#1729—431no—
193#1729—431no—
194#1729D4311yescharacteristic
195#1728—431no—
196C2×C43—24no—
197C2×C43C2×#38711yescharacteristic
198C2×C43#292512yes—
199C2×C43#292911yescharacteristic
200C2×C43#293011yescharacteristic
201C2×C43#296212yes—
202C22×M16—431no—
203C22×M16C2×D4311yescharacteristic
204C23×C8—431no—
205C23×C8C2×D4311yescharacteristic
206C2×#117—431no—
207C2×#117C2×D4311yescharacteristic
208C22×C42—431no—
209C2×C4⋊C8—432no—
210C2×C4⋊C8—432no—
211C2×C4⋊C8—864no—
212#405—864no—
213C2×#97—432no—
214C2×C4×C8—432no—
215#389—432no—
216#389—432no—
217#385—432no—
218#385—432no—
219C4×C4⋊C4—434no—
220#336—432no—
221#336—434no—
222#336—434no—
223#336—432no—
224#336C2×D4314yes—
225C43#2102411yescharacteristic, complemented, Sylow
226C23×C4—431no—
227C23×C4—431no—
228C23×C4C22×D4311yescharacteristic
229C2×M16—22no—
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—434no—
233C2×M16—862no—
234C2×M16—862no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8—22no—
238C22×C8—434no—
239C22×C8—431no—
240C22×C8—431no—
241C22×C8—432no—
242C22×C8—862no—
243C22×C8—862no—
244C22×C8C22×D4312yes—
245C22×C8C22×D4312yes—
246#117—22no—
247#117—22no—
248#117—862no—
249#117—862no—
250C2×C4⋊C4—432no—
251C2×C4⋊C4—434no—
252C2×C4⋊C4—434no—
253C2×C4⋊C4C4×D4311yescharacteristic
254C2×C4⋊C4C4×D4311yescharacteristic
255C2×C22⋊C4—432no—
256C2×C22⋊C4C4×D4312yes—
257C2×C42—432no—
258C2×C42—432no—
259C2×C42—432no—
260C2×C42—862no—
261C2×C42—862no—
262C2×C42C22×D4312yes—
263C4⋊C8—864no—
264C4⋊C8—864no—
265#97—864no—
266C4×C8—864no—
267#95—434no—
268#95—434no—
269C24C2×C4×D4311yescharacteristic
270C22×C4—432no—
271C22×C4—432no—
272C22×C4—434no—
273C22×C4—864no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—1722no—
277C22×C4C2×C4×D4312yes—
278C22×C4C2×C4×D4312yes—
279C22×C4C2×C4×D4311yescharacteristic
280C22×C4#1062189812yes—
281C22×C4#1062189812yes—
282C22×C4D4×D4312yes—
283C22×C4#1062190012yes—
284C22×C4#1062190012yes—
285C22×C4Q8×D4312yes—
286C22×C4C23×D4311yescharacteristic
287M16—44no—
288M16—868no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—44no—
296C2×C8—432no—
297C2×C8—432no—
298C2×C8—434no—
299C2×C8—868no—
300C2×C8—862no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—861no—
305C2×C8—862no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—868no—
309C4⋊C4—864no—
310C4⋊C4—1724no—
311C22⋊C4—24no—
312C22⋊C4—864no—
313C42—22no—
314C42—22no—
315C42—864no—
316C42—862no—
317C42—862no—
318C42—862no—
319C42—862no—
320C23—22no—
321C23—22no—
322C23#1306328212yes—
323C23(C22⋊D43)⋊C412yes—
324C23#1306329012yes—
325C23C22×C4×D4311yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—434no—
331C2×C4—868no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—864no—
335C2×C4—862no—
336C2×C4—864no—
337C2×C4—862no—
338C2×C4—864no—
339C2×C4—862no—
340C2×C4—1724no—
341C2×C4#1306328212yes—
342C2×C4(C22⋊D43)⋊C412yes—
343C2×C4#1306329012yes—
344C2×C4#1306330314yes—
345C2×C4#1306330714yes—
346C2×C4#1306331514yes—
347C2×C4#1306331814yes—
348C2×C4C2×D4×D4311yescharacteristic
349C2×C4C2×Q8×D4311yescharacteristic
350C2×C4C2×#1062190011yescharacteristic
351C2×C4C2×#1062190011yescharacteristic
352C2×C4C2×#1062189811yescharacteristic
353C2×C4C2×#1062189811yescharacteristic
354C8—42no—
355C8—42no—
356C8—864no—
357C8—862no—
358C8—862no—
359C22—24no—
360C22—24no—
361C22—22no—
362C22—22no—
363C22#1458278114yes—
364C22C2×#1306328211yescharacteristic
365C22C2×(C22⋊D43)⋊C411yescharacteristic
366C22C2×#1306329011yescharacteristic
367C22#131×D4312yes—
368C22#1458366412yes—
369C4—42no—
370C4—42no—
371C4—864no—
372C4—1724no—
373C4—1722no—
374C4#1458278114yes—
375C4C2×#1306330311yescharacteristic
376C4C2×#1306330711yescharacteristic
377C4C2×#1306331511yescharacteristic
378C4C2×#1306331811yescharacteristic
379C2—24no—
380C2C2×#1458278111yescharacteristic
381C2#1914325912yes—
382C2#1914329211yescharacteristic
383C2#1914330111yescharacteristic
384C2#1914354112yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1729C2
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenter#1729D43
hypocenterC43#21024
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1729

Complements

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

NH ≅ G/Ntype
4. #19135157C2semidirect
5. #19135150C2semidirect
225. C43#21024semidirect

Maximal subgroups

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

subgroupindex
C22×Dic43⋊C82
C2×#145828552
#191370772
#191351572
#191351502
#191342932
#191342912
#191342882
C43×#17292
#2102443