Finite Group Databasebeta

← #25014801

Subgroups — #25014801

Order 11008.

438 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143287C211yesmaximal, characteristic
2#19136360C211yesmaximal, characteristic, complemented
3#19136223C211yesmaximal, characteristic, complemented
4#19136205C211yesmaximal, characteristic, complemented
5#19136205C211yesmaximal, characteristic, complemented
6#19136199C211yesmaximal, characteristic, complemented
7C43×#2117C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9#14583406C411yescharacteristic
10C2×#13063265C2211yescharacteristic
11C2×#13063265C2211yescharacteristic
12#14582968—22no—
13C8×C22⋊D43—22no—
14#14582927C411yescharacteristic
15#14582866C411yescharacteristic
16#14582862C411yescharacteristic
17#14582854C2211yescharacteristic
18#14582719—22no—
19#14582683—22no—
20(C2×D43)⋊C16—22no—
21(C2×D43)⋊C16—22no—
22#14582676—22no—
23C2×#131×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C43×#350—22no—
27C22×C4×D43C2×C411yescharacteristic
28C2×#10621877C2×C411yescharacteristic
29C22×C43⋊C8C2×C411yescharacteristic
30C2×C8×D43—21no—
31C2×C8×D43—21no—
32C2×C8×D43—21no—
33C2×C8×D43—21no—
34C2×C8×D43—21no—
35C2×C8×D43—21no—
36#13063306—21no—
37#13063301—21no—
38#13063296—21no—
39#13063293—21no—
40C4×C22⋊D43—22no—
41#13063284C2×C411yescharacteristic
42#13063265—21no—
43#13063265—21no—
44#13063265—21no—
45#13063265—21no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16D412yescomplemented
48Dic43⋊C8—22no—
49C22⋊(C43⋊C8)—22no—
50(C2×D43)⋊C8—22no—
51#13063235D412yes—
52C8×Dic43D412yes—
53C2×#41×C43C2×C411yescharacteristic
54#131×C43—21no—
55#131×C43—21no—
56#131×C43—21no—
57#131×C43—21no—
58C2×M16×C43—21no—
59C2×M16×C43C2×C411yescharacteristic
60C22×C8×C43—21no—
61C22×C8×C43C2311yescharacteristic
62M32×C43—21no—
63M32×C43—21no—
64M32×C43—21no—
65M32×C43—21no—
66C2×C16×C43—21no—
67C2×C16×C43D412yescomplemented
68C23×D43M1611yescharacteristic
69#41×C43—21no—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43—21no—
73C2×Q8×C43M1611yescharacteristic
74C2×D4×C43—21no—
75C2×D4×C43M1611yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43C22×C411yescharacteristic
78C2×C22⋊D43—22no—
79C22×Dic43M1611yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86M16×C43—21no—
87M16×C43—21no—
88M16×C43—41no—
89M16×C43—41no—
90C2×C8×C43—21no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43#4111yescharacteristic
98C2×C8×C43#4111yescharacteristic
99C22⋊Dic43—22no—
100C22⋊Dic43—21no—
101(C2×D43)⋊C4—22no—
102C4⋊Dic43—21no—
103Dic43⋊C4—22no—
104C4×Dic43C22⋊C412yes—
105#10621877—21no—
106#10621877—21no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8C22⋊C412yes—
111C8×D43—41no—
112C8×D43—41no—
113C8×D43—41no—
114C8×D43—41no—
115C16×C43—22no—
116C16×C43—41no—
117C43⋊C16—22no—
118C43⋊C16—41no—
119C23×C43—21no—
120C23×C43C2×M1611yescharacteristic
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—42no—
125Q8×C43—21no—
126Q8×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—41no—
130D4×C43—41no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C2×M1611yescharacteristic
138C2×C4×C43#13111yescharacteristic
139C2×C4×C43#13111yescharacteristic
140C22⋊D43—44no—
141C2×Dic43—22no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C4×D43—41no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C8×C43—41no—
150C8×C43#12111yescharacteristic
151C8×C43#12111yescharacteristic
152C8×C43#12411yescharacteristic
153C8×C43#12711yescharacteristic
154C43⋊C8—22no—
155C43⋊C8—41no—
156#13200—431nomaximal, Sylow
157C22×C43—41no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43#40711yescharacteristic
161C22×C43#43511yescharacteristic
162C22×C43#43511yescharacteristic
163C2×D43—22no—
164C2×D43—22no—
165C2×D43—22no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C4×C43—41no—
171C4×C43#39011yescharacteristic
172C4×C43#40811yescharacteristic
173C4×C43#43511yescharacteristic
174C4×C43#43511yescharacteristic
175Dic43—42no—
176Dic43—41no—
177#2929—431no—
178#2153—431no—
179#2117—431no—
180#2117D4311yescharacteristic, complemented
181#2112—431no—
182#2112—431no—
183#2110—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—81no—
188C2×C43#195511yescharacteristic
189D43—42no—
190C2×#131C2×D4311yescharacteristic
191C23×C8—431no—
192#525—431no—
193C2×M32—431no—
194C2×M32—431no—
195C2×M32C2×D4311yescharacteristic
196C2×M32C2×D4311yescharacteristic
197#435—862no—
198C8×D4—862no—
199#424—431no—
200#408—431no—
201#407—431no—
202#405—431no—
203#364—862no—
204#350—22no—
205#350—862no—
206C22⋊C16—862no—
207C22⋊C16—862no—
208#347—862no—
209C43#1320011yescharacteristic, complemented, Sylow
210C2×#41C4×D4311yescharacteristic
211C23×C4—431no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—21no—
216C2×M16—21no—
217C2×M16—431no—
218C2×M16C4×D4311yescharacteristic
219C22×C8—21no—
220C22×C8—431no—
221C22×C8—861no—
222C22×C8—861no—
223C22×C8—861no—
224C22×C8—861no—
225C22×C8—861no—
226C22×C8—861no—
227C22×C8C22×D4311yescharacteristic
228#123—861no—
229C22⋊Q8—861no—
230#121—861no—
231#120—861no—
232C4×D4—862no—
233#117—431no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—861no—
239M32—861no—
240M32—861no—
241M32—861no—
242C2×C16—21no—
243C2×C16—432no—
244C2×C16—861no—
245C2×C16C22⋊D4312yescomplemented
246C4⋊C8—862no—
247C22⋊C8—862no—
248C22⋊C8—862no—
249#97—432no—
250C4×C8—432no—
251C24—431no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256C2×Q8#1062187211yescharacteristic
257C2×D4—21no—
258C2×D4—862no—
259C2×D4#1062187211yescharacteristic
260C22×C4—21no—
261C22×C4—431no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4C2×C4×D4311yescharacteristic
269M16—21no—
270M16—21no—
271M16—41no—
272M16—41no—
273M16—861no—
274M16—861no—
275C2×C8—21no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—432no—
279C2×C8—861no—
280C2×C8—861no—
281C2×C8—861no—
282C2×C8—1721no—
283C2×C8—1721no—
284C2×C8—1721no—
285C2×C8—1721no—
286C2×C8#1062189811yescharacteristic
287C2×C8D4×D4311yescharacteristic
288C2×C8D4×D4311yescharacteristic
289C2×C8D4×D4311yescharacteristic
290C2×C8#1062190011yescharacteristic
291C2×C8C2×C22⋊D4311yescharacteristic
292C4⋊C4—862no—
293C4⋊C4—861no—
294C22⋊C4—862no—
295C22⋊C4—862no—
296C22⋊C4—861no—
297C42—432no—
298C16—22no—
299C16—41no—
300C16—862no—
301C16—1721no—
302C23—21no—
303C23—861no—
304C23—861no—
305C23—861no—
306C23—1722no—
307C23M16×D4311yescharacteristic
308Q8—21no—
309Q8—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—1724no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—862no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4C22⋊C4×D4311yescharacteristic
327C2×C4(C22⋊D43)⋊C411yescharacteristic
328C2×C4C4×C22⋊D4311yescharacteristic
329C2×C4C2×#1062187211yescharacteristic
330C2×C4#1306333111yescharacteristic
331C2×C4#1306333311yescharacteristic
332C8—41no—
333C8—862no—
334C8—1721no—
335C8#1306329711yescharacteristic
336C8#1306329811yescharacteristic
337C8#1306331111yescharacteristic
338C8#1306332111yescharacteristic
339C22—41no—
340C22—42no—
341C22—41no—
342C22—862no—
343C22—862no—
344C22—862no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22#1458286111yescharacteristic
350C22#1458296811yescharacteristic
351C22#1458297311yescharacteristic
352C4—41no—
353C4—1722no—
354C4—1721no—
355C4#1458279911yescharacteristic
356C4#1458286411yescharacteristic
357C4#1458296711yescharacteristic
358C4#1458297011yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—1722no—
364C2#1913539111yescharacteristic
subgroupG/H
centerC8#13063321
commutatorC22×C4×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2117C2
socleC2×C43#1955
prime radical#14583406C4
cosocleC22×C8×C43C23
hypercenter#2117D43
hypocenterC43#13200
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. #19136360C2semidirect
3. #19136223C2semidirect
4. #19136205C2semidirect
5. #19136205C2semidirect
6. #19136199C2semidirect
7. C43×#2117C2semidirect
47. C2×C43⋊C16D4semidirect
67. C2×C16×C43D4semidirect
180. #2117D43semidirect
209. C43#13200semidirect
245. C2×C16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191432872
#191363602
#191362232
#191362052
#191361992
C43×#21172
#1320043