Finite Group Databasebeta

← #25013243

Subgroups — #25013243

Order 11008.

422 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143396C211yesmaximal, characteristic
2#19136381C211yesmaximal, characteristic, complemented
3C2×#14582709C211yesmaximal, characteristic
4#19135336C211yesmaximal, characteristic, complemented
5#19132701C211yesmaximal, characteristic, complemented
6#19132678C211yesmaximal, characteristic, complemented
7C43×#2139C211yesmaximal, characteristic
8#41×Dic43—21no—
9C2×#13063265C2211yescharacteristic
10#14583011—21no—
11#14583006—21no—
12#14583000—21no—
13#14583000—21no—
14#14582937C2211yescharacteristic
15C2×#13063257C2211yescharacteristic
16#14582895—21no—
17C2×#13063235C2211yescharacteristic
18#14582795—21no—
19#14582726—21no—
20#14582724—21no—
21#14582709C414yescomplemented
22#14582661—21no—
23C2×#135×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C43×#358—21no—
27C43×#357—21no—
28C22×C43⋊C8D411yescharacteristic
29Q8×Dic43—21no—
30Q8×Dic43—21no—
31D4×Dic43—21no—
32D4×Dic43—21no—
33D4×Dic43—41no—
34D4×Dic43—41no—
35#13063284—21no—
36#13063284—41no—
37C2×C4⋊Dic43—21no—
38C2×Dic43⋊C4—41no—
39C2×C4×Dic43—41no—
40C2×C4×Dic43D411yescharacteristic
41#13063265—21no—
42#13063265C2×C412yescomplemented
43C2×C43⋊C16—21no—
44#13063259D411yescharacteristic
45#13063259D411yescharacteristic
46#13063257—21no—
47#13063257—21no—
48#13063257C2×C412yescomplemented
49#13063249—21no—
50#13063249—21no—
51#13063246—21no—
52#13063246—21no—
53#13063235—21no—
54#13063235—21no—
55C43⋊#95—41no—
56C2×#41×C43—21no—
57#135×C43—21no—
58#135×C43—21no—
59#135×C43C2×C412yes—
60#135×C43Q812yes—
61C2×Q16×C43D411yescharacteristic
62C2×SD16×C43—21no—
63C2×D8×C43D411yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C2×C4⋊C4×C43—21no—
66M32×C43—21no—
67M32×C43—21no—
68C2×C16×C43—21no—
69#107×C43—21no—
70#107×C43—21no—
71#41×C43—22no—
72#41×C43—22no—
73#41×C43—41no—
74#41×C43—41no—
75C2×Q8×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81C22×Dic43—41no—
82C22×Dic43—41no—
83C22×Dic43—41no—
84C22×Dic43D811yescharacteristic
85C22×Dic43D811yescharacteristic
86Q16×C43—21no—
87Q16×C43C4⋊C412yescomplemented
88SD16×C43—22no—
89SD16×C43—22no—
90D8×C43—21no—
91D8×C43C4⋊C412yescomplemented
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×Q811yescharacteristic
96C2×C8×C43#4111yescharacteristic
97C2×C8×C43#4111yescharacteristic
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C22⋊Dic43—41no—
103C4⋊Dic43—22no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109Dic43⋊C4—82no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—41no—
113C4×Dic43—41no—
114C4×Dic43—41no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C16×C43—41no—
119C43⋊C16—22no—
120C23×C43—41no—
121C23×C43C2×D811yescharacteristic
122Q8×C43—22no—
123Q8×C43—41no—
124D4×C43—22no—
125D4×C43—42no—
126D4×C43—42no—
127D4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43C22⋊Q811yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—82no—
148C2×Dic43—82no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151C8×C43C2×C4⋊C411yescharacteristic
152C8×C43C4×D411yescharacteristic
153C8×C43C22⋊Q811yescharacteristic
154C8×C43#12311yescharacteristic
155C43⋊C8—41no—
156#12943—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—42no—
160C22×C43—81no—
161C22×C43—81no—
162C22×C43C4×D811yescharacteristic
163C22×C43#44711yescharacteristic
164C22×C43#47411yescharacteristic
165C4×C43—42no—
166C4×C43—161no—
167C4×C43#38511yescharacteristic
168C4×C43#44011yescharacteristic
169C4×C43#45211yescharacteristic
170C4×C43#47811yescharacteristic
171Dic43—41no—
172Dic43—41no—
173Dic43—82no—
174Dic43—81no—
175Dic43—81no—
176#2943—431no—
177#2159—431no—
178C2×#360—431no—
179#2139D4311yescharacteristic
180#1944—431no—
181#1386—431no—
182#1377—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—82no—
186C2×C43#186211yescharacteristic
187C2×C43#219011yescharacteristic
188C2×C43#219111yescharacteristic
189C2×#135C2×D4311yescharacteristic
190C4×#41—861no—
191C2×M32—431no—
192C2×M32C2×D4311yescharacteristic
193#442—861no—
194#441—861no—
195#440—861no—
196#440—861no—
197#427—431no—
198C2×#107C2×D4311yescharacteristic
199C2×#106—431no—
200#416—861no—
201C2×#97—431no—
202#389—861no—
203#367—861no—
204#366—861no—
205#360—434no—
206#358—21no—
207#357—21no—
208#340—861no—
209C43#1294311yescharacteristic, complemented, Sylow
210C2×#41—21no—
211#135—21no—
212#135—21no—
213#135Dic8612yes—
214#135C4×D4312yes—
215C2×Q16C22⋊D4311yescharacteristic
216C2×SD16—21no—
217C2×D8C22⋊D4311yescharacteristic
218C22×C8—431no—
219C22×C8C22×D4311yescharacteristic
220C4×Q8—861no—
221C4×Q8—861no—
222C4×D4—861no—
223C4×D4—861no—
224C4×D4—1721no—
225C4×D4—1721no—
226#117—861no—
227#117—1721no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—1721no—
231C2×C42—431no—
232C2×C42—1721no—
233M32—21no—
234M32—21no—
235M32—432no—
236M32—861no—
237C2×C16—21no—
238C2×C16—861no—
239#107—21no—
240#107—21no—
241#107—431no—
242#107—431no—
243#106—432no—
244#106—861no—
245#106—861no—
246#103—861no—
247#103—861no—
248#102—861no—
249#102—861no—
250#97—861no—
251#97—861no—
252#95—1721no—
253#41—22no—
254#41—22no—
255#41—41no—
256#41—41no—
257C2×Q8—21no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—1721no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4D4×D4311yescharacteristic
268Q16—21no—
269Q16Dic43⋊C412yescomplemented
270SD16—22no—
271SD16—22no—
272D8—21no—
273D8Dic43⋊C412yescomplemented
274C2×C8—861no—
275C2×C8—861no—
276C2×C8—861no—
277C2×C8C2×Dic8611yescharacteristic
278C2×C8C2×C4×D4311yescharacteristic
279C2×C8D4×D4311yescharacteristic
280C2×C8#1062190011yescharacteristic
281C2×C8#1062190011yescharacteristic
282C2×C8C2×C22⋊D4311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—862no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—3442no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C42—861no—
296C42—861no—
297C42—1721no—
298C42—1721no—
299C42—1721no—
300C16—41no—
301C16—862no—
302C23—41no—
303C23D8×D4311yescharacteristic
304Q8—22no—
305Q8—41no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—3442no—
321C2×C4—3442no—
322C2×C4—1722no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4(C22⋊D43)⋊C411yescharacteristic
328C2×C4#1306329311yescharacteristic
329C2×C4#1306330211yescharacteristic
330C2×C4#1306334611yescharacteristic
331C2×C4#1306334911yescharacteristic
332C2×C4#1306335411yescharacteristic
333C8—1721no—
334C8C2×Dic43⋊C411yescharacteristic
335C8(C22⋊D43)⋊C411yescharacteristic
336C8#1306330211yescharacteristic
337C8#1306330611yescharacteristic
338C22—21no—
339C22—21no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22#1458297911yescharacteristic
344C22#1458303111yescharacteristic
345C22#1458317711yescharacteristic
346C4—42no—
347C4—161no—
348C4—3442no—
349C4—3441no—
350C4—3441no—
351C4—1721no—
352C4—1721no—
353C4#1458277111yescharacteristic
354C4#1458299611yescharacteristic
355C4#1458305811yescharacteristic
356C4#1458320111yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2#1913484011yescharacteristic
361C2#1913653911yescharacteristic
362C2#1913654411yescharacteristic
subgroupG/H
centerC22#14583031
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2139C2
socleC22×C43#447
prime radicalC2×#135×C43C22
cosocleC22×C8×C43C23
hypercenter#2139D43
hypocenterC43#12943
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
2. #19136381C2semidirect
4. #19135336C2semidirect
5. #19132701C2semidirect
6. #19132678C2semidirect
21. #14582709C4semidirect
42. #13063265C2×C4semidirect
48. #13063257C2×C4semidirect
87. Q16×C43C4⋊C4semidirect
91. D8×C43C4⋊C4semidirect
209. C43#12943semidirect
269. Q16Dic43⋊C4semidirect
273. D8Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
#191433962
#191363812
C2×#145827092
#191353362
#191327012
#191326782
C43×#21392
#1294343