Finite Group Databasebeta

← #24991795

Subgroups — #24991795

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic
2#19143536C211yesmaximal, characteristic, complemented
3#19135392C211yesmaximal, characteristic
4#19133021C211yesmaximal, characteristic
5#19132492C211yesmaximal, characteristic, complemented
6#19132439C211yesmaximal, characteristic, complemented
7C43×#1542C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9#14583227C412yes—
10#14583186—21no—
11#14583101—21no—
12#14583049C412yes—
13#14583030—22no—
14#14583030—22no—
15C4×#10621884—22no—
16#14582952C2211yescharacteristic
17#14582926—21no—
18#14582923C2211yescharacteristic
19C2×(C2×D43)⋊C8—21no—
20C2×(C2×D43)⋊C8—21no—
21#14582855—21no—
22C2×#13063236C2211yescharacteristic
23#14582628—22no—
24C43×#533C2211yescharacteristic
25C43×#431C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C43×#333—21no—
28C43×#332—21no—
29C22×D172C2×C411yescharacteristic
30C22×C4×D43—21no—
31C2×#10621884—22no—
32C2×#10621877—21no—
33C22×C43⋊C8D411yescharacteristic
34C22×C43⋊C8D411yescharacteristic
35C4×D172—21no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×(C2×D43)⋊C4—21no—
41#13063256—22no—
42C4⋊(C43⋊C8)—24no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D412yes—
46#13063249—22no—
47#13063245—22no—
48C22⋊(C43⋊C8)C2×C412yes—
49(C2×D43)⋊C8—42no—
50(C2×D43)⋊C8—42no—
51#13063236—22no—
52#13063236—21no—
53#13063236—21no—
54C4×C43⋊C8—22no—
55C4×C43⋊C8—21no—
56C22×C8×C43—21no—
57C4⋊Q8×C43D411yescharacteristic
58C4⋊Q8×C43D411yescharacteristic
59#125×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43C2×C412yes—
62C4×Q8×C43—21no—
63C4×Q8×C43D412yes—
64#117×C43—21no—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71C23×D43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43C22⋊C412yes—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×Dic43—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172—42no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43C22⋊C412yes—
97C22⋊C4×C43—22no—
98C42×C43—22no—
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103#10621884—44no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108#10621877—41no—
109#10621877—41no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8SD1612yescomplemented
118C23×C43C4×D411yescharacteristic
119C22×D43—22no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126Q8×C43—42no—
127Q8×C43—81no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C2×C4×C43C2×SD1611yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145D172—22no—
146D172—22no—
147D172—41no—
148D172—41no—
149C4×D43—81no—
150C4×D43—81no—
151C4×D43—81no—
152C4×D43—81no—
153C8×C43—81no—
154C8×C43—81no—
155C43⋊C8—22no—
156C43⋊C8—42no—
157C43⋊C8—41no—
158C43⋊C8—42no—
159#9050—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#38611yescharacteristic
163C22×C43C4×SD1611yescharacteristic
164C22×C43#44011yescharacteristic
165C2×D43—42no—
166C2×D43—42no—
167C2×D43—42no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—42no—
177C4×C43—42no—
178C4×C43#44811yescharacteristic
179C4×C43#44911yescharacteristic
180C4×C43#46011yescharacteristic
181C4×C43#46411yescharacteristic
182Dic43—81no—
183#3101—431no—
184#2961—431no—
185#1955—431no—
186#1542D4311yescharacteristic, complemented
187#1486—431no—
188#1301—431no—
189#1281—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#188011yescharacteristic
193C2×C43#188111yescharacteristic
194C2×C43#189111yescharacteristic
195D43—82no—
196#533C2×D4311yescharacteristic
197C2×C4×D4—431no—
198#483—432no—
199#476—861no—
200#461—861no—
201#450—432no—
202#446—862no—
203#446—862no—
204C4×SD16—862no—
205#431—431no—
206#431C2×D4311yescharacteristic
207#424—861no—
208#423—431no—
209C2×C4⋊C8C2×D4311yescharacteristic
210C2×C22⋊C8—861no—
211C2×C22⋊C8—861no—
212#405—861no—
213C2×#97—431no—
214#333—21no—
215#332—21no—
216D4⋊C8—862no—
217C43#905011yescharacteristic, complemented, Sylow
218C22×D4—431no—
219C23×C4—861no—
220C2×SD16—862no—
221C2×M16—861no—
222C22×C8—21no—
223C22×C8—431no—
224C22×C8—431no—
225C4⋊Q8C22⋊D4311yescharacteristic
226C4⋊Q8C22⋊D4311yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8C4×D4312yes—
230C4×Q8—21no—
231C4×Q8D17212yes—
232C4×D4—861no—
233C4×D4—861no—
234C4×D4—861no—
235C4×D4—861no—
236#117—21no—
237C2×C4⋊C4—431no—
238C2×C22⋊C4—861no—
239C2×C42C22×D4311yescharacteristic
240#106—862no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—432no—
245C4⋊C8—864no—
246C4⋊C8—861no—
247C4⋊C8—861no—
248#103—862no—
249#102—862no—
250C22⋊C8—21no—
251C22⋊C8—432no—
252C22⋊C8—1722no—
253C22⋊C8—1722no—
254#97—862no—
255#97—861no—
256#97—861no—
257C4×C8—21no—
258C4×C8—862no—
259C4×C8—861no—
260C24—861no—
261C2×Q8—21no—
262C2×Q8(C2×D43)⋊C412yes—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—1722no—
266C22×C4—861no—
267C22×C4—1721no—
268C22×C4—1721no—
269C22×C4—1721no—
270C22×C4—1721no—
271C22×C4—1721no—
272C22×C4—1721no—
273C22×C4C2×C4×D4311yescharacteristic
274C22×C4D4×D4311yescharacteristic
275C22×C4#1062190011yescharacteristic
276SD16—1724no—
277M16—1721no—
278M16—1721no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—432no—
284C2×C8—861no—
285C2×C8—861no—
286C2×C8—862no—
287C2×C8—862no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—861no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4(C2×D43)⋊C412yes—
299C22⋊C4—22no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C42—22no—
303C42C2×D17211yescharacteristic
304C42D4×D4311yescharacteristic
305C42#1062190011yescharacteristic
306C42C2×C22⋊D4311yescharacteristic
307C23—862no—
308C23—1721no—
309C23—1721no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23—1721no—
314C23(C22⋊D43)⋊C411yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—862no—
318D4—862no—
319D4—1721no—
320D4—1721no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4C2×(C2×D43)⋊C411yescharacteristic
333C2×C4(C22⋊D43)⋊C411yescharacteristic
334C2×C4#1306329511yescharacteristic
335C2×C4#1306329711yescharacteristic
336C2×C4#1306329711yescharacteristic
337C2×C4#1306330911yescharacteristic
338C2×C4SD16×D4311yescharacteristic
339C2×C4#1306334811yescharacteristic
340C2×C4#1306335211yescharacteristic
341C2×C4#1306335711yescharacteristic
342C8—81no—
343C8—81no—
344C8—862no—
345C8—1722no—
346C8—1721no—
347C8—1722no—
348C22—21no—
349C22—21no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22—3441no—
354C22—1722no—
355C22—1722no—
356C22—1722no—
357C22#1458277611yescharacteristic
358C22#1458298411yescharacteristic
359C22#1458300211yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—3441no—
367C4#1458303911yescharacteristic
368C4#1458304711yescharacteristic
369C4#1458309711yescharacteristic
370C4#1458312311yescharacteristic
371C2—21no—
372C2—21no—
373C2—3442no—
374C2#1913494811yescharacteristic
375C2#1913495511yescharacteristic
376C2#1913501111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1542C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1542D43
hypocenterC43#9050
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
2. #19143536C2semidirect
5. #19132492C2semidirect
6. #19132439C2semidirect
7. C43×#1542C2semidirect
117. C2×C43⋊C8SD16semidirect
186. #1542D43semidirect
217. C43#9050semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191435362
#191353922
#191330212
#191324922
#191324392
C43×#15422
#905043