Finite Group Databasebeta

← #24996648

Subgroups — #24996648

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582783C211yesmaximal, characteristic
2#19134357C211yesmaximal, characteristic
3#19132437C212yesmaximal
4#19132437C212yesmaximal
5C43×#1797C211yesmaximal, characteristic
6C22×Dic43⋊C4C411yescharacteristic
7C22×Dic43⋊C4C411yescharacteristic
8C2×C22⋊(C43⋊C8)C2212yes—
9C2×#13063236—21no—
10#14582783—21no—
11#14582783—21no—
12#14582783—21no—
13#14582783—21no—
14C2×C43⋊#95C411yescharacteristic
15C2×C43⋊#95C411yescharacteristic
16C2×C43⋊#95C2211yescharacteristic
17C2×C43⋊#95C2211yescharacteristic
18#14582654—21no—
19C22×C42×C43C2211yescharacteristic
20C2×C4⋊C8×C43—21no—
21C2×C22⋊C8×C43C2212yes—
22C43×#336—21no—
23C23×Dic43C2×C411yescharacteristic
24C23×Dic43C2×C411yescharacteristic
25C23×Dic43C2×C411yescharacteristic
26C23×Dic43C2×C411yescharacteristic
27C22×C43⋊C8—22no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—42no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)Q814yes—
37#13063236—42no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43C2311yescharacteristic
49C22×C8×C43—22no—
50C2×C42×C43—42no—
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C4⋊C8×C43—42no—
56C22⋊C8×C43—24no—
57C24×C43C22×C411yescharacteristic
58C22×C4×C43—22no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—22no—
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×Q812yes—
74C22×C4×C43#4112yes—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—22no—
82C22×Dic43—22no—
83C22×Dic43—41no—
84C22×Dic43—41no—
85C22×Dic43—41no—
86C22×Dic43—41no—
87C22×Dic43—41no—
88C22×Dic43—41no—
89C22×Dic43—41no—
90C22×Dic43—41no—
91C22×Dic43M1612yes—
92C22×Dic43M1612yes—
93C2×C8×C43—42no—
94C2×C8×C43—42no—
95C2×C8×C43—42no—
96C42×C43—22no—
97C42×C43—22no—
98C42×C43—41no—
99C42×C43—41no—
100Dic43⋊C4—24no—
101Dic43⋊C4—24no—
102Dic43⋊C4—42no—
103Dic43⋊C4—42no—
104C2×C43⋊C8—24no—
105C2×C43⋊C8—42no—
106C2×C43⋊C8—42no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43C2×C22⋊C411yescharacteristic
112C23×C43C4×Q812yes—
113C23×C43C2×M1611yescharacteristic
114C23×C43C2×M1611yescharacteristic
115C23×C43#13112yes—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—44no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43#9912yes—
137C2×C4×C43C22⋊Q812yes—
138C2×C4×C43#12411yescharacteristic
139C2×C4×C43C4⋊Q811yescharacteristic
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—82no—
157C2×Dic43—82no—
158C8×C43—82no—
159C43⋊C8—44no—
160#9881—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—22no—
166C22×C43—22no—
167C22×C43—22no—
168C22×C43—22no—
169C22×C43#39111yescharacteristic
170C22×C43#40711yescharacteristic
171C22×C43#40811yescharacteristic
172C22×C43C2×#9911yescharacteristic
173C22×C43#41011yescharacteristic
174C22×C43#41311yescharacteristic
175C22×C43#41311yescharacteristic
176C22×C43#44612yes—
177C22×C43#44612yes—
178C4×C43—22no—
179C4×C43—22no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43—41no—
185Dic43—42no—
186Dic43—42no—
187Dic43—81no—
188Dic43—81no—
189C2×#387—431no—
190#1797D4311yescharacteristic
191#1749—431no—
192#1280—432no—
193#1280—432no—
194C2×C43—22no—
195C2×C43—22no—
196C2×C43#146411yescharacteristic
197C2×C43#146511yescharacteristic
198C2×C43#146811yescharacteristic
199C2×C43#147311yescharacteristic
200C2×C43#198511yescharacteristic
201C2×C43#199611yescharacteristic
202C2×C43#199811yescharacteristic
203C22×C4⋊C4—431no—
204C22×C4⋊C4—431no—
205C22×C42C2×D4311yescharacteristic
206C2×C4⋊C8—21no—
207C2×C22⋊C8—432no—
208C2×C22⋊C8C2×D4312yes—
209C2×#97—861no—
210#387—861no—
211#387—861no—
212#387—861no—
213#387—861no—
214C2×#95—431no—
215C2×#95—431no—
216C2×#95—431no—
217C2×#95—431no—
218#336—21no—
219#336—861no—
220C43#988111yescharacteristic, complemented, Sylow
221C23×C4—431no—
222C23×C4—431no—
223C23×C4—431no—
224C23×C4—431no—
225C23×C4C4×D4311yescharacteristic
226C23×C4C4×D4311yescharacteristic
227C23×C4C22×D4311yescharacteristic
228C22×C8—22no—
229C22×C8—862no—
230C2×C4⋊C4—862no—
231C2×C4⋊C4—862no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—1722no—
237C2×C42—42no—
238C2×C42D17211yescharacteristic
239C2×C42D17211yescharacteristic
240C2×C42C22⋊D4311yescharacteristic
241C2×C42C22⋊D4311yescharacteristic
242C4⋊C8—42no—
243C22⋊C8—24no—
244C22⋊C8—434no—
245C22⋊C8—862no—
246#97—1722no—
247#95—861no—
248#95—861no—
249#95—861no—
250#95—861no—
251#95—861no—
252#95—861no—
253#95—861no—
254#95—861no—
255C24C2×C4×D4311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—432no—
266C22×C4—432no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—862no—
272C22×C4—862no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—1721no—
276C22×C4—1721no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4—1721no—
280C22×C4—1721no—
281C22×C4—1721no—
282C22×C4—1721no—
283C22×C4(C2×D43)⋊C411yescharacteristic
284C22×C4(C2×D43)⋊C411yescharacteristic
285C22×C4(C2×D43)⋊C411yescharacteristic
286C22×C4(C2×D43)⋊C411yescharacteristic
287C22×C4C2×D17211yescharacteristic
288C22×C4#1062190012yes—
289C22×C4Q8×D4312yes—
290C22×C4C2×C22⋊D4311yescharacteristic
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—864no—
295C2×C8—1722no—
296C2×C8—1722no—
297C4⋊C4—864no—
298C4⋊C4—864no—
299C4⋊C4—1722no—
300C4⋊C4—1722no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×(C2×D43)⋊C411yescharacteristic
310C23#1306329012yes—
311C23M16×D4311yescharacteristic
312C23M16×D4311yescharacteristic
313C23#1306333112yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—862no—
335C2×C4—862no—
336C2×C4—3442no—
337C2×C4—3442no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4#1306323912yes—
353C2×C4#1306330512yes—
354C2×C4#1306331211yescharacteristic
355C2×C4#1306332311yescharacteristic
356C8—82no—
357C8—1724no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—21no—
365C22—21no—
366C22#1458280411yescharacteristic
367C22#1458286211yescharacteristic
368C22#1458286511yescharacteristic
369C22C2×#1306323911yescharacteristic
370C22#1458287211yescharacteristic
371C22#1458288111yescharacteristic
372C22#1458288111yescharacteristic
373C22#1458302812yes—
374C22#1458302812yes—
375C4—22no—
376C4—21no—
377C4—22no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3441no—
383C4—3441no—
384C4—1722no—
385C4—1722no—
386C2—22no—
387C2—22no—
388C2#1913292711yescharacteristic
389C2#1913293111yescharacteristic
390C2#1913294111yescharacteristic
391C2#1913296211yescharacteristic
392C2#1913553411yescharacteristic
393C2#1913557911yescharacteristic
394C2#1913558711yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutator, prime radicalC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1797C2
socleC23×C43C2×C22⋊C4
cosocleC23×C4×C43C23
hypercenter#1797D43
hypocenterC43#9881
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
220. C43#9881semidirect

Maximal subgroups

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

subgroupindex
C2×#145827832
#191343572
#191324372
C43×#17972
#988143