Finite Group Databasebeta

← #24984638

Subgroups — #24984638

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137138C211yesmaximal, characteristic
2#19134737C211yesmaximal, characteristic, complemented
3#19134443C211yesmaximal, characteristic, complemented
4#19132421C211yesmaximal, characteristic, complemented
5#19132415C211yesmaximal, characteristic
6#19132415C211yesmaximal, characteristic
7C43×#1272C211yesmaximal, characteristic, complemented
8C2×#13063314C411yescharacteristic
9C2×Q8×Dic43C411yescharacteristic
10C2×#13063287C411yescharacteristic
11C2×Dic43⋊C8—21no—
12C2×C8×Dic43—21no—
13#14582801C2211yescharacteristic
14#14582791—21no—
15#14582791—21no—
16#14582764C411yescharacteristic
17#14582746—21no—
18#14582746—21no—
19C42×Dic43C2211yescharacteristic
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
24C43×#391C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063314—22no—
32#13063314C814yescomplemented
33Q8×Dic43—42no—
34#13063287—42no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
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—
42C2×C4×Dic43—21no—
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49Dic43⋊C8—24no—
50C8×Dic43—42no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C22×Q8×C43C2×C411yescharacteristic
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#95×C43—21no—
59#95×C43—21no—
60C23×D43—21no—
61C2×Q8×C43—21no—
62C2×Q8×C43—41no—
63C2×Q8×C43—41no—
64C2×Q8×C43C2×C812yes—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×D172—21no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172C2×C812yes—
79C2×C4×D43—42no—
80C2×C4×D43—42no—
81C2×C4×D43—42no—
82C2×C8×C43—22no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C4⋊C4×C43—41no—
89C42×C43—41no—
90(C2×D43)⋊C4—24no—
91(C2×D43)⋊C4—24no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—42no—
97C4⋊Dic43—42no—
98C4⋊Dic43—41no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—22no—
104C4×Dic43—22no—
105C4×Dic43—41no—
106C4×Dic43—42no—
107C4×Dic43C2×C812yes—
108C4×Dic43M1612yes—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C22×D43—22no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123Q8×C43—42no—
124Q8×C43—42no—
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—22no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43C22×C811yescharacteristic
138C2×C4×C43C2×M1611yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43C22⋊C812yes—
155C2×Dic43C22⋊C812yes—
156C2×Dic43#10012yes—
157C2×Dic43#10412yes—
158D172—42no—
159D172—42no—
160C4×D43—84no—
161C8×C43—42no—
162C8×C43—81no—
163C43⋊C8—42no—
164C43⋊C8—81no—
165#7584—431nomaximal, Sylow
166C22×C43C2×C22⋊C811yescharacteristic
167C22×C43#41011yescharacteristic
168C22×C43C2×#10011yescharacteristic
169C22×C43#41611yescharacteristic
170C22×C43#41711yescharacteristic
171C22×C43C2×#10411yescharacteristic
172C22×C43#42111yescharacteristic
173C2×D43—42no—
174C2×D43—42no—
175C2×D43—42no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—81no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—42no—
187C4×C43—81no—
188Dic43—22no—
189Dic43—22no—
190Dic43—22no—
191Dic43—22no—
192Dic43—81no—
193C4×#124—431no—
194#1839—431no—
195C4×C4⋊C8—431no—
196#1272—431no—
197#1272D4311yescharacteristic, complemented
198#1270—431no—
199#1270—431no—
200C2×C43#146011yescharacteristic
201C2×C43#147611yescharacteristic
202C2×C43#147711yescharacteristic
203C2×C43#150911yescharacteristic
204C2×C43#152111yescharacteristic
205C2×C43#152711yescharacteristic
206C2×C43#155111yescharacteristic
207D43—82no—
208C2×#124—431no—
209C2×C4×Q8—431no—
210C2×C4×D4—431no—
211C2×C4⋊C8—861no—
212C2×C4×C8—861no—
213#391C2×D4311yescharacteristic
214#390—431no—
215#388—861no—
216#388—861no—
217#382—431no—
218C4×C22⋊C4—861no—
219C4×C22⋊C4—861no—
220C43—431no—
221#336—431no—
222#336—431no—
223#336—861no—
224#336—861no—
225#336C2×D4311yescharacteristic
226#336C2×D4311yescharacteristic
227C43#758411yescharacteristic, complemented, Sylow
228C22×Q8C4×D4311yescharacteristic
229C22×D4—431no—
230C23×C4—861no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—861no—
234C22×C8—861no—
235#124—434no—
236#124—862no—
237C4×Q8—1722no—
238C4×D4—1722no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4C4×D4311yescharacteristic
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C42—431no—
248C2×C42—431no—
249C2×C42—431no—
250C2×C42—431no—
251C2×C42—431no—
252C2×C42—431no—
253C2×C42—861no—
254C2×C42C22×D4311yescharacteristic
255C4⋊C8—864no—
256C4×C8—1722no—
257#95—21no—
258#95—21no—
259#95—861no—
260#95—861no—
261C24—861no—
262C2×Q8—21no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8C8×D4312yes—
266C2×D4—432no—
267C2×D4—861no—
268C2×D4—1721no—
269C2×D4—1721no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—861no—
277C22×C4—1722no—
278C22×C4—1722no—
279C22×C4—1722no—
280C22×C4C2×C4×D4311yescharacteristic
281C22×C4D4×D4311yescharacteristic
282C22×C4D4×D4311yescharacteristic
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—862no—
290C2×C8—1721no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—41no—
296C4⋊C4—1721no—
297C4⋊C4—1722no—
298C22⋊C4—864no—
299C22⋊C4—864no—
300C22⋊C4—1722no—
301C22⋊C4—1721no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C42—41no—
306C42—432no—
307C42—432no—
308C42—862no—
309C42—862no—
310C42—861no—
311C42—861no—
312C42—861no—
313C42—861no—
314C42—1721no—
315C42—1722no—
316C23—862no—
317C23—1721no—
318C23—1721no—
319C23—1721no—
320C23—1721no—
321C23—1721no—
322C23—1721no—
323C23C22⋊C4×D4311yescharacteristic
324Q8—42no—
325Q8—42no—
326D4—1722no—
327D4—1722no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—432no—
341C2×C4—432no—
342C2×C4—432no—
343C2×C4—432no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—3444no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4C2×C8×D4311yescharacteristic
357C2×C4M16×D4311yescharacteristic
358C2×C4#1306334611yescharacteristic
359C2×C4#1306334811yescharacteristic
360C2×C4#1306335211yescharacteristic
361C2×C4#1306335711yescharacteristic
362C8—42no—
363C8—81no—
364C8—3441no—
365C8—1722no—
366C22—3441no—
367C22—3441no—
368C22—3441no—
369C22—3441no—
370C22—1722no—
371C22—1722no—
372C22—1722no—
373C22C22⋊C8×D4311yescharacteristic
374C22#1458287111yescharacteristic
375C22#100×D4311yescharacteristic
376C22#1458289411yescharacteristic
377C22#1458289911yescharacteristic
378C22#104×D4311yescharacteristic
379C22#1458291411yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—862no—
389C4—862no—
390C4—862no—
391C4—862no—
392C4—3441no—
393C2—3442no—
394C2#1913291411yescharacteristic
395C2#1913297611yescharacteristic
396C2#1913298111yescharacteristic
397C2#1913311911yescharacteristic
398C2#1913317111yescharacteristic
399C2#1913319111yescharacteristic
400C2#1913328911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7584
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #19134737C2semidirect
3. #19134443C2semidirect
4. #19132421C2semidirect
7. C43×#1272C2semidirect
32. #13063314C8semidirect
197. #1272D43semidirect
227. C43#7584semidirect

Maximal subgroups

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

subgroupindex
#191371382
#191347372
#191344432
#191324212
#191324152
C43×#12722
#758443