Finite Group Databasebeta

← #24989931

Subgroups — #24989931

Order 11008.

786 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 119 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×#14582761C211yesmaximal, characteristic
2#19134504C212yesmaximal
3#19132438C211yesmaximal, characteristic, complemented
4#19132437C212yesmaximal, complemented
5C43×#1280C211yesmaximal, characteristic, complemented
6C23×C4×D43C2211yescharacteristic
7C22×(C2×D43)⋊C4C412yes—
8C2×C22⋊(C43⋊C8)C2212yes—
9C2×(C2×D43)⋊C8—24no—
10#14582761—24no—
11C2×C43⋊#95C412yes—
12C2×C43⋊#95C2211yescharacteristic
13C2×C22⋊C8×C43C2212yes—
14C2×#95×C43C2211yescharacteristic
15C24×D43C2×C411yescharacteristic
16C23×Dic43C2×C412yes—
17C23×Dic43C2×C411yescharacteristic
18C22×C4×D43—22no—
19C22×C4×D43—21no—
20C22×C4×D43—21no—
21C22×C4×D43—44no—
22C22×C4×D43D414yes—
23C22×C43⋊C8—22no—
24C2×(C2×D43)⋊C4—22no—
25C2×(C2×D43)⋊C4—22no—
26C2×(C2×D43)⋊C4—44no—
27C22⋊(C43⋊C8)—22no—
28C22⋊(C43⋊C8)—22no—
29(C2×D43)⋊C8—48no—
30C43⋊#95—22no—
31C43⋊#95—24no—
32C23×C4×C43C2×C412yes—
33C23×C4×C43C2311yescharacteristic
34C22×C8×C43—22no—
35C22⋊C8×C43—22no—
36C22⋊C8×C43—22no—
37#95×C43—22no—
38C24×C43C22×C411yescharacteristic
39C23×D43—21no—
40C23×D43—21no—
41C23×D43—24no—
42C23×D43—22no—
43C23×D43—22no—
44C23×D43—41no—
45C23×D43—41no—
46C23×D43C22⋊C412yes—
47C22×C4×C43—22no—
48C22×C4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43—42no—
51C22×C4×C43—42no—
52C22×C4×C43—42no—
53C22×C4×C43C2×D412yes—
54C22×C4×C43#4112yes—
55C22×C4×C43#4111yescharacteristic
56C22×C4×C43#4111yescharacteristic
57C22×Dic43—22no—
58C22×Dic43—21no—
59C22×Dic43—21no—
60C22×Dic43—22no—
61C22×Dic43—22no—
62C22×Dic43—42no—
63C22×Dic43—42no—
64C22×Dic43—42no—
65C22×Dic43C22⋊C412yes—
66C2×C4×D43—24no—
67C2×C4×D43—24no—
68C2×C4×D43—28no—
69C2×C4×D43—44no—
70C2×C4×D43—48no—
71C2×C4×D43—44no—
72C2×C4×D43—44no—
73C2×C8×C43—44no—
74C2×C8×C43—42no—
75(C2×D43)⋊C4—44no—
76(C2×D43)⋊C4—44no—
77C2×C43⋊C8—44no—
78C2×C43⋊C8—42no—
79C23×C43—22no—
80C23×C43—21no—
81C23×C43—21no—
82C23×C43C2×C22⋊C411yescharacteristic
83C23×C43#11711yescharacteristic
84C23×C43#11711yescharacteristic
85C23×C43#13112yes—
86C23×C43#13112yes—
87C22×D43—24no—
88C22×D43—24no—
89C22×D43—22no—
90C22×D43—22no—
91C22×D43—22no—
92C22×D43—22no—
93C22×D43—22no—
94C22×D43—22no—
95C22×D43—44no—
96C22×D43—44no—
97C22×D43—44no—
98C22×D43—44no—
99C22×D43—42no—
100C22×D43—42no—
101C22×D43—41no—
102C22×D43—42no—
103C22×D43—41no—
104C22×D43#9914yes—
105C2×C4×C43—24no—
106C2×C4×C43—42no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—82no—
113C2×C4×C43—82no—
114C2×C4×C43#12312yes—
115C2×C4×C43#12312yes—
116C2×Dic43—22no—
117C2×Dic43—24no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—82no—
124C2×Dic43—82no—
125C4×D43—48no—
126C4×D43—48no—
127C8×C43—82no—
128C43⋊C8—82no—
129#8702—431nomaximal, Sylow
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—22no—
135C22×C43—22no—
136C22×C43—22no—
137C22×C43—22no—
138C22×C43#38111yescharacteristic
139C22×C43#40812yes—
140C22×C43C2×#9912yes—
141C22×C43#41311yescharacteristic
142C22×C43#41311yescharacteristic
143C22×C43#43311yescharacteristic
144C22×C43#43312yes—
145C22×C43#43311yescharacteristic
146C2×D43—24no—
147C2×D43—24no—
148C2×D43—24no—
149C2×D43—44no—
150C2×D43—48no—
151C2×D43—44no—
152C2×D43—42no—
153C2×D43—42no—
154C2×D43—42no—
155C2×D43—42no—
156C4×C43—22no—
157C4×C43—22no—
158C4×C43—82no—
159Dic43—42no—
160Dic43—82no—
161C2×#381—431no—
162#1779—432no—
163#1280—432no—
164#1280—431no—
165#1280D4311yescharacteristic, complemented
166C2×C43—21no—
167C2×C43—22no—
168C2×C43—21no—
169C2×C43#146812yes—
170C2×C43#146812yes—
171C2×C43#181811yescharacteristic
172C2×C43#181911yescharacteristic
173C2×C43#182211yescharacteristic
174D43—44no—
175C24×C4—431no—
176C22×C22⋊C4—432no—
177C2×C22⋊C8—432no—
178C2×C22⋊C8—864no—
179C2×C22⋊C8C2×D4312yes—
180#381—864no—
181C2×#95—431no—
182C2×#95—432no—
183C2×#95C2×D4311yescharacteristic
184C43#870211yescharacteristic, complemented, Sylow
185C25—431no—
186C23×C4—431no—
187C23×C4—434no—
188C23×C4—432no—
189C23×C4—862no—
190C23×C4—861no—
191C23×C4—861no—
192C23×C4—1724no—
193C23×C4C4×D4312yes—
194C23×C4C22×D4311yescharacteristic
195C22×C8—22no—
196C22×C8—862no—
197C2×C22⋊C4—862no—
198C2×C22⋊C4—862no—
199C2×C22⋊C4—1724no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202C22⋊C8—862no—
203C22⋊C8—862no—
204C22⋊C8—1728no—
205#95—22no—
206#95—864no—
207#95—862no—
208C24—432no—
209C24—864no—
210C24—861no—
211C24—861no—
212C24—862no—
213C24—862no—
214C24—1721no—
215C24—1721no—
216C24C2×C4×D4311yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—432no—
224C22×C4—868no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4—864no—
228C22×C4—864no—
229C22×C4—862no—
230C22×C4—862no—
231C22×C4—862no—
232C22×C4—1724no—
233C22×C4—1728no—
234C22×C4—1724no—
235C22×C4—1724no—
236C22×C4—1722no—
237C22×C4—1722no—
238C22×C4—1722no—
239C22×C4#1062189812yes—
240C22×C4D4×D4312yes—
241C22×C4#1062190011yescharacteristic
242C22×C4#1062190211yescharacteristic
243C2×C8—44no—
244C2×C8—42no—
245C2×C8—1724no—
246C2×C8—1722no—
247C22⋊C4—1724no—
248C22⋊C4—1724no—
249C23—22no—
250C23—21no—
251C23—21no—
252C23—434no—
253C23—864no—
254C23—864no—
255C23—862no—
256C23—862no—
257C23—862no—
258C23—862no—
259C23—862no—
260C23—862no—
261C23—1724no—
262C23—1724no—
263C23—1724no—
264C23—1724no—
265C23—1722no—
266C23—1722no—
267C23—1721no—
268C23—1722no—
269C23—1721no—
270C23C22⋊C4×D4311yescharacteristic
271C23#1306328211yescharacteristic
272C23#1306328311yescharacteristic
273C23#1306333112yes—
274C23#1306333312yes—
275C2×C4—24no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—864no—
285C2×C4—862no—
286C2×C4—3442no—
287C2×C4—3442no—
288C2×C4—1728no—
289C2×C4—1728no—
290C2×C4—1722no—
291C2×C4—1722no—
292C2×C4—1722no—
293C2×C4—1722no—
294C2×C4—1722no—
295C2×C4#1306330712yes—
296C2×C4#1306331012yes—
297C8—82no—
298C8—3442no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—864no—
308C22—864no—
309C22—864no—
310C22—1724no—
311C22—1728no—
312C22—1724no—
313C22—1722no—
314C22—1722no—
315C22—1722no—
316C22—1722no—
317C22#1458276111yescharacteristic
318C22#1458286412yes—
319C22#99×D4312yes—
320C22#1458288011yescharacteristic
321C22#1458288211yescharacteristic
322C22#1458295811yescharacteristic
323C22#1458295912yes—
324C22#1458296111yescharacteristic
325C4—22no—
326C4—22no—
327C4—82no—
328C4—3442no—
329C4—1722no—
330C2—21no—
331C2—22no—
332C2—21no—
333C2—1724no—
334C2#1913294012yes—
335C2#1913294212yes—
336C2#1913466511yescharacteristic
337C2#1913466811yescharacteristic
338C2#1913467711yescharacteristic
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#8702
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
165. #1280D43semidirect
184. C43#8702semidirect

Maximal subgroups

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

subgroupindex
C2×#145827612
#191345042
#191324382
#191324372
C43×#12802
#870243