Finite Group Databasebeta

← #24989937

Subgroups — #24989937

Order 11008.

830 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582758C211yesmaximal, characteristic
2#19134504C212yesmaximal
3#19132438C211yesmaximal, characteristic, complemented
4#19132437C212yesmaximal, complemented
5C43×#1280C211yesmaximal, characteristic, complemented
6C23×C4×D43C2211yescharacteristic
7C22×Dic43⋊C4C412yes—
8C22×(C2×D43)⋊C4C412yes—
9C2×C22⋊(C43⋊C8)C2212yes—
10C2×(C2×D43)⋊C8—22no—
11C2×(C2×D43)⋊C8—22no—
12#14582758—22no—
13#14582758—22no—
14C2×C43⋊#95C2211yescharacteristic
15C2×C22⋊C8×C43C2212yes—
16C2×#95×C43C2211yescharacteristic
17C24×D43C2×C411yescharacteristic
18C23×Dic43C2×C411yescharacteristic
19C23×Dic43C2×C412yes—
20C22×C4×D43—22no—
21C22×C4×D43—21no—
22C22×C4×D43—21no—
23C22×C4×D43—44no—
24C22×C4×D43D412yes—
25C22×C4×D43D412yes—
26C22×C43⋊C8—22no—
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—44no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4—44no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35(C2×D43)⋊C8—44no—
36(C2×D43)⋊C8—44no—
37C43⋊#95—22no—
38C23×C4×C43C2×C412yes—
39C23×C4×C43C2311yescharacteristic
40C22×C8×C43—22no—
41C22⋊C8×C43—22no—
42C22⋊C8×C43—22no—
43#95×C43—22no—
44C24×C43C22×C411yescharacteristic
45C23×D43—21no—
46C23×D43—21no—
47C23×D43—22no—
48C23×D43—22no—
49C23×D43—22no—
50C23×D43—22no—
51C23×D43—42no—
52C23×D43C22⋊C411yescharacteristic
53C23×D43C22⋊C411yescharacteristic
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43C2×D412yes—
61C22×C4×C43#4112yes—
62C22×C4×C43#4111yescharacteristic
63C22×C4×C43#4111yescharacteristic
64C22×Dic43—24no—
65C22×Dic43—22no—
66C22×Dic43—21no—
67C22×Dic43—21no—
68C22×Dic43—22no—
69C22×Dic43—22no—
70C22×Dic43—42no—
71C22×Dic43—42no—
72C22×Dic43C22⋊C412yes—
73C2×C4×D43—22no—
74C2×C4×D43—22no—
75C2×C4×D43—22no—
76C2×C4×D43—22no—
77C2×C4×D43—24no—
78C2×C4×D43—24no—
79C2×C4×D43—42no—
80C2×C4×D43—42no—
81C2×C4×D43—48no—
82C2×C4×D43—44no—
83C2×C4×D43—44no—
84C2×C8×C43—42no—
85C2×C8×C43—42no—
86C2×C8×C43—42no—
87(C2×D43)⋊C4—44no—
88(C2×D43)⋊C4—44no—
89Dic43⋊C4—44no—
90Dic43⋊C4—44no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—42no—
93C2×C43⋊C8—42no—
94C23×C43—22no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43C2×C22⋊C411yescharacteristic
98C23×C43#11711yescharacteristic
99C23×C43#11711yescharacteristic
100C23×C43#13112yes—
101C23×C43#13112yes—
102C22×D43—24no—
103C22×D43—24no—
104C22×D43—21no—
105C22×D43—21no—
106C22×D43—22no—
107C22×D43—22no—
108C22×D43—22no—
109C22×D43—22no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—44no—
113C22×D43—44no—
114C22×D43—44no—
115C22×D43—44no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—41no—
119C22×D43—42no—
120C22×D43—41no—
121C22×D43#10012yes—
122C22×D43#10112yes—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—82no—
132C2×C4×C43—82no—
133C2×C4×C43#12312yes—
134C2×C4×C43#12312yes—
135C2×Dic43—24no—
136C2×Dic43—24no—
137C2×Dic43—22no—
138C2×Dic43—22no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—82no—
143C2×Dic43—82no—
144C2×Dic43#9914yes—
145C4×D43—44no—
146C4×D43—44no—
147C4×D43—44no—
148C4×D43—44no—
149C8×C43—82no—
150C43⋊C8—82no—
151#8704—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—22no—
157C22×C43—22no—
158C22×C43—22no—
159C22×C43—22no—
160C22×C43#38111yescharacteristic
161C22×C43#40812yes—
162C22×C43C2×#9912yes—
163C22×C43C2×#10011yescharacteristic
164C22×C43C2×#10111yescharacteristic
165C22×C43#43311yescharacteristic
166C22×C43#43312yes—
167C22×C43#43311yescharacteristic
168C2×D43—22no—
169C2×D43—22no—
170C2×D43—24no—
171C2×D43—24no—
172C2×D43—44no—
173C2×D43—48no—
174C2×D43—44no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—42no—
180C2×D43—42no—
181C4×C43—22no—
182C4×C43—22no—
183C4×C43—82no—
184Dic43—24no—
185Dic43—82no—
186C2×#380—431no—
187#1779—432no—
188#1280—432no—
189#1280—431no—
190#1280D4311yescharacteristic, complemented
191C2×C43—21no—
192C2×C43—22no—
193C2×C43—21no—
194C2×C43#147112yes—
195C2×C43#147212yes—
196C2×C43#181811yescharacteristic
197C2×C43#181911yescharacteristic
198C2×C43#182111yescharacteristic
199D43—42no—
200D43—42no—
201C24×C4—431no—
202C22×C4⋊C4—432no—
203C22×C22⋊C4—432no—
204C2×C22⋊C8—432no—
205C2×C22⋊C8—862no—
206C2×C22⋊C8—862no—
207C2×C22⋊C8C2×D4312yes—
208#380—862no—
209#380—862no—
210C2×#95—431no—
211C2×#95C2×D4311yescharacteristic
212C43#870411yescharacteristic, complemented, Sylow
213C25—431no—
214C23×C4—431no—
215C23×C4—432no—
216C23×C4—432no—
217C23×C4—432no—
218C23×C4—862no—
219C23×C4—861no—
220C23×C4—861no—
221C23×C4—1724no—
222C23×C4C4×D4312yes—
223C23×C4C22×D4311yescharacteristic
224C22×C8—22no—
225C22×C8—862no—
226C2×C4⋊C4—862no—
227C2×C4⋊C4—862no—
228C2×C4⋊C4—1724no—
229C2×C22⋊C4—862no—
230C2×C22⋊C4—862no—
231C2×C22⋊C4—1724no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—862no—
235C22⋊C8—862no—
236C22⋊C8—1724no—
237C22⋊C8—1724no—
238#95—22no—
239#95—862no—
240C24—431no—
241C24—431no—
242C24—862no—
243C24—862no—
244C24—861no—
245C24—861no—
246C24—862no—
247C24—862no—
248C24—1722no—
249C24C2×C4×D4311yescharacteristic
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—432no—
257C22×C4—864no—
258C22×C4—864no—
259C22×C4—864no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—862no—
263C22×C4—862no—
264C22×C4—862no—
265C22×C4—862no—
266C22×C4—862no—
267C22×C4—862no—
268C22×C4—862no—
269C22×C4—1722no—
270C22×C4—1722no—
271C22×C4—1728no—
272C22×C4—1724no—
273C22×C4—1724no—
274C22×C4—1722no—
275C22×C4—1722no—
276C22×C4#1062189812yes—
277C22×C4D4×D4312yes—
278C22×C4#1062190011yescharacteristic
279C22×C4#1062190211yescharacteristic
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—1722no—
284C2×C8—1722no—
285C2×C8—1722no—
286C4⋊C4—1724no—
287C4⋊C4—1724no—
288C22⋊C4—1724no—
289C22⋊C4—1724no—
290C23—22no—
291C23—21no—
292C23—21no—
293C23—432no—
294C23—432no—
295C23—864no—
296C23—864no—
297C23—862no—
298C23—862no—
299C23—862no—
300C23—862no—
301C23—861no—
302C23—861no—
303C23—861no—
304C23—861no—
305C23—1724no—
306C23—1724no—
307C23—1724no—
308C23—1724no—
309C23—1722no—
310C23—1722no—
311C23—1721no—
312C23—1722no—
313C23—1721no—
314C23C22⋊C4×D4311yescharacteristic
315C23#1306328211yescharacteristic
316C23#1306328311yescharacteristic
317C23#1306333112yes—
318C23#1306333312yes—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—434no—
330C2×C4—864no—
331C2×C4—864no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—3442no—
335C2×C4—3442no—
336C2×C4—1724no—
337C2×C4—1724no—
338C2×C4—1724no—
339C2×C4—1724no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4#1306330712yes—
344C2×C4#1306331012yes—
345C8—82no—
346C8—3442no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—864no—
356C22—864no—
357C22—862no—
358C22—862no—
359C22—1724no—
360C22—1728no—
361C22—1724no—
362C22—1722no—
363C22—1722no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22#1458276111yescharacteristic
369C22#1458286412yes—
370C22#99×D4312yes—
371C22#100×D4311yescharacteristic
372C22#101×D4311yescharacteristic
373C22#1458295811yescharacteristic
374C22#1458295912yes—
375C22#1458296111yescharacteristic
376C4—22no—
377C4—22no—
378C4—82no—
379C4—864no—
380C4—3442no—
381C2—21no—
382C2—22no—
383C2—21no—
384C2—1722no—
385C2—1722no—
386C2#1913295312yes—
387C2#1913295712yes—
388C2#1913466511yescharacteristic
389C2#1913466811yescharacteristic
390C2#1913467411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1280C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1280D43
hypocenterC43#8704
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #19132438C2semidirect
4. #19132437C2semidirect
5. C43×#1280C2semidirect
190. #1280D43semidirect
212. C43#8704semidirect

Maximal subgroups

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

subgroupindex
C2×#145827582
#191345042
#191324382
#191324372
C43×#12802
#870443