Finite Group Databasebeta

← #24995608

Subgroups — #24995608

Order 11008.

526 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142967C211yesmaximal, characteristic
2C4×#13063236C211yesmaximal, characteristic, complemented
3C2×#14582640C212yesmaximal, complemented
4C2×#14582638C212yesmaximal
5C43×#1767C211yesmaximal, characteristic, complemented
6C2×#13063317C2211yescharacteristic
7C2×#13063313C2211yescharacteristic
8C2×#13063236—21no—
9C2×#13063236C2212yes—
10C2×C4×C43⋊C8—21no—
11#14582805C411yescharacteristic
12#14582805C411yescharacteristic
13#14582801C411yescharacteristic
14#14582801C411yescharacteristic
15#14582790—21no—
16#14582790—21no—
17#14582790—21no—
18#14582790—21no—
19#14582640—24no—
20#14582638—24no—
21C2×C4⋊C8×C43—21no—
22C2×#97×C43C2212yes—
23C43×C43C2211yescharacteristic
24C43×#336—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27C22×C43⋊C8—22no—
28#13063317—22no—
29#13063317—22no—
30#13063313—22no—
31#13063313—22no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42#13063236—24no—
43#13063236—22no—
44#13063236D414yes—
45C4×C43⋊C8—24no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×C8×C43—22no—
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C2×C42×C43D411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—24no—
59#97×C43—22no—
60#97×C43—22no—
61C23×D43—21no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×D172—22no—
73C2×D172—41no—
74C2×D172—41no—
75C2×Dic86—22no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×C8×C43—24no—
79C2×C8×C43—42no—
80C2×C8×C43—42no—
81C42×C43—22no—
82C42×C43—22no—
83C42×C43—22no—
84C42×C43—41no—
85C42×C43—41no—
86C42×C43—41no—
87C42×C43C2×D412yes—
88C42×C43#4112yes—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96C4⋊Dic43—22no—
97C4⋊Dic43—22no—
98Dic43⋊C4—42no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101C2×C43⋊C8—24no—
102C2×C43⋊C8—24no—
103C2×C43⋊C8—24no—
104C23×C43C2×C22⋊C411yescharacteristic
105C22×D43—41no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43—41no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
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#10412yes—
128C2×C4×C43#10412yes—
129C2×C4×C43#10412yes—
130C2×C4×C43C4×D412yes—
131C2×C4×C43#12112yes—
132C2×C4×C43#12411yescharacteristic
133C2×C4×C43#12711yescharacteristic
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143D172—82no—
144Dic86—82no—
145C8×C43—44no—
146C43⋊C8—28no—
147#9687—431nomaximal, Sylow
148C22×C43#39011yescharacteristic
149C22×C43#41311yescharacteristic
150C22×C43#41311yescharacteristic
151C22×C43C2×#10411yescharacteristic
152C22×C43C2×#10411yescharacteristic
153C22×C43C2×#10411yescharacteristic
154C22×C43#42111yescharacteristic
155C2×D43—81no—
156C2×D43—81no—
157C2×D43—81no—
158C2×D43—81no—
159C2×D43—81no—
160C2×D43—81no—
161C2×D43—81no—
162C4×C43—22no—
163C4×C43—22no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—22no—
167C4×C43—22no—
168C4×C43—22no—
169C4×C43—41no—
170Dic43—81no—
171Dic43—81no—
172Dic43—81no—
173#2861—431no—
174#1767D4311yescharacteristic, complemented
175C4×#97—431no—
176C2×#330—432no—
177C2×#329—432no—
178C2×C43#152411yescharacteristic
179C2×C43#152411yescharacteristic
180C2×C43#152911yescharacteristic
181C2×C43#153211yescharacteristic
182C2×C43#196211yescharacteristic
183C2×C43#196711yescharacteristic
184C2×C43#198011yescharacteristic
185D43—161no—
186C2×#125—431no—
187C2×#124—431no—
188C2×C4⋊C8—21no—
189C2×#97—432no—
190C2×#97—861no—
191C2×#97C2×D4312yes—
192C2×C4×C8—861no—
193#391—431no—
194#391—431no—
195#390—431no—
196#390—431no—
197#388—861no—
198#388—861no—
199#388—861no—
200#388—861no—
201C43C2×D4311yescharacteristic
202#336—21no—
203#330—864no—
204#329—864no—
205C43#968711yescharacteristic, complemented, Sylow
206C22×Q8—431no—
207C22×D4—431no—
208C22×C8—22no—
209C22×C8—862no—
210#125—862no—
211#125—862no—
212#124—862no—
213#124—862no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C22⋊C4—861no—
224C2×C42C4×D4311yescharacteristic
225C2×C42C4×D4311yescharacteristic
226C2×C42D17211yescharacteristic
227C2×C42D17211yescharacteristic
228C2×C42C22⋊D4311yescharacteristic
229C2×C42C22⋊D4311yescharacteristic
230C2×C42C22×D4311yescharacteristic
231C4⋊C8—24no—
232#97—22no—
233#97—22no—
234#97—434no—
235#97—864no—
236#97—862no—
237C4×C8—864no—
238#95—861no—
239#95—861no—
240#95—861no—
241#95—861no—
242C24—861no—
243C2×Q8—862no—
244C2×Q8—1721no—
245C2×Q8—1721no—
246C2×D4—862no—
247C2×D4—1721no—
248C2×D4—1721no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4(C2×D43)⋊C411yescharacteristic
253C22×C4(C2×D43)⋊C411yescharacteristic
254C22×C4(C2×D43)⋊C411yescharacteristic
255C22×C4(C2×D43)⋊C411yescharacteristic
256C22×C4C2×C4×D4311yescharacteristic
257C22×C4C2×D17211yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259C2×C8—24no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—864no—
263C2×C8—864no—
264C2×C8—864no—
265C4⋊C4—862no—
266C4⋊C4—862no—
267C4⋊C4—1722no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C22⋊C4—1722no—
271C22⋊C4—1722no—
272C22⋊C4—1722no—
273C22⋊C4—1722no—
274C22⋊C4—1722no—
275C22⋊C4—1721no—
276C22⋊C4—1721no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—41no—
281C42—41no—
282C42—41no—
283C42D4×D4312yes—
284C42#1062190212yes—
285C23—1721no—
286C23—1721no—
287C23—1721no—
288C23—1721no—
289C23—1721no—
290C23—1721no—
291C23—1721no—
292C23C2×(C2×D43)⋊C411yescharacteristic
293Q8—3442no—
294D4—3442no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4#1306325112yes—
320C2×C4#1306325112yes—
321C2×C4#1306325312yes—
322C2×C4#1306328712yes—
323C2×C4#1306330012yes—
324C2×C4#1306331411yescharacteristic
325C2×C4#1306332111yescharacteristic
326C8—44no—
327C8—868no—
328C22—3441no—
329C22—3441no—
330C22—3441no—
331C22—3441no—
332C22—3441no—
333C22—3441no—
334C22—3441no—
335C22#1458280011yescharacteristic
336C22#1458288111yescharacteristic
337C22#1458288111yescharacteristic
338C22C2×#1306325111yescharacteristic
339C22C2×#1306325111yescharacteristic
340C22C2×#1306325311yescharacteristic
341C22#1458291711yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—22no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—3441no—
351C4—3441no—
352C4—3441no—
353C2—6881no—
354C2#1913318111yescharacteristic
355C2#1913318411yescharacteristic
356C2#1913320311yescharacteristic
357C2#1913321611yescharacteristic
358C2#1913542211yescharacteristic
359C2#1913544211yescharacteristic
360C2#1913551311yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1767C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1767D43
hypocenterC43#9687
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. C4×#13063236C2semidirect
3. C2×#14582640C2semidirect
5. C43×#1767C2semidirect
174. #1767D43semidirect
205. C43#9687semidirect

Maximal subgroups

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

subgroupindex
#191429672
C4×#130632362
C2×#145826402
C2×#145826382
C43×#17672
#968743