Finite Group Databasebeta

← #25014799

Subgroups — #25014799

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#19143289C211yesmaximal, characteristic
2#19136360C211yesmaximal, characteristic, complemented
3#19136224C211yesmaximal, characteristic, complemented
4#19136222C211yesmaximal, characteristic, complemented
5#19136206C211yesmaximal, characteristic, complemented
6#19136199C211yesmaximal, characteristic, complemented
7C43×#2112C211yesmaximal, characteristic, complemented
8C2×#13063331C2211yescharacteristic
9#14583410C411yescharacteristic
10C2×#13063265C2211yescharacteristic
11C2×#13063265C2211yescharacteristic
12#14582970—22no—
13C8×C22⋊D43—22no—
14#14582925C411yescharacteristic
15#14582865C411yescharacteristic
16#14582863C411yescharacteristic
17#14582854C2211yescharacteristic
18#14582719—22no—
19#14582684—22no—
20#14582682—22no—
21C22⋊(C43⋊C16)—22no—
22#14582676—22no—
23C23×C8×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C43×C22⋊C16—22no—
27C2×#10621898C2×C411yescharacteristic
28#13063331—21no—
29#13063331—21no—
30#13063331—21no—
31#13063331—21no—
32C2×#10621877C2×C411yescharacteristic
33C2×#10621877C2×C411yescharacteristic
34C2×#10621872—21no—
35C2×C8×D43—21no—
36#13063308—21no—
37#13063304—21no—
38#13063299—21no—
39#13063294—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—
53C23×C4×C43C2×C411yescharacteristic
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C22×C8×C43—21no—
60C22×C8×C43C2×C411yescharacteristic
61C22×C8×C43C2311yescharacteristic
62M32×C43—21no—
63M32×C43—21no—
64M32×C43—21no—
65M32×C43—21no—
66C2×C16×C43—21no—
67C2×C16×C43D412yescomplemented
68C24×C43M1611yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43M1611yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C2×C22⋊D43—22no—
78C2×C22⋊D43—21no—
79#10621898—21no—
80#10621898—21no—
81#10621898—21no—
82#10621898—21no—
83C2×D172M1611yescharacteristic
84C2×C4×D43—21no—
85C2×Dic86M1611yescharacteristic
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
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—
107#10621877—21no—
108#10621877—21no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8C22⋊C412yes—
111#10621872—41no—
112#10621872—41no—
113C8×D43—41no—
114C8×D43—41no—
115C16×C43—22no—
116C16×C43—41no—
117C43⋊C16—22no—
118C43⋊C16—41no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—42no—
123C23×C43C2×M1611yescharacteristic
124C22×D43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C2×M1611yescharacteristic
136C2×C4×C43#13111yescharacteristic
137C2×C4×C43#13111yescharacteristic
138C22⋊D43—44no—
139C22⋊D43—41no—
140C22⋊D43—41no—
141C2×Dic43—22no—
142C2×Dic43—21no—
143D172—21no—
144D172—21no—
145C4×D43—41no—
146C4×D43—41no—
147Dic86—21no—
148Dic86—21no—
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—22no—
158C22×C43—22no—
159C22×C43—22no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43#40711yescharacteristic
166C22×C43#43511yescharacteristic
167C22×C43#43511yescharacteristic
168C2×D43—42no—
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#2117—431no—
181#2112—431no—
182#2112D4311yescharacteristic, complemented
183#2110—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—42no—
188C2×C43#195511yescharacteristic
189D43—81no—
190C2×#131—431no—
191C23×C8C2×D4311yescharacteristic
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—862no—
205#350—862no—
206C22⋊C16—22no—
207C22⋊C16—862no—
208#347—862no—
209C43#1320011yescharacteristic, complemented, Sylow
210C2×#41—431no—
211C23×C4C4×D4311yescharacteristic
212#131—861no—
213#131—861no—
214#131—861no—
215#131—861no—
216C2×M16—431no—
217C2×M16—431no—
218C2×M16—861no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—861no—
226C22×C8C4×D4311yescharacteristic
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#1062187211yescharacteristic
252#41—861no—
253#41—861no—
254#41—861no—
255#41—861no—
256C2×Q8—431no—
257C2×D4—431no—
258C2×D4—862no—
259C2×D4—861no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—861no—
267C22×C4#1062187211yescharacteristic
268C22×C4C2×C4×D4311yescharacteristic
269M16—861no—
270M16—861no—
271M16—861no—
272M16—861no—
273M16—1721no—
274M16—1721no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—432no—
283C2×C8—861no—
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—21no—
304C23—21no—
305C23—42no—
306C23—861no—
307C23C2×#1062187211yescharacteristic
308Q8—861no—
309Q8—861no—
310D4—861no—
311D4—861no—
312D4—1724no—
313D4—1721no—
314D4—1721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—862no—
323C2×C4—861no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4C22⋊C4×D4311yescharacteristic
327C2×C4(C22⋊D43)⋊C411yescharacteristic
328C2×C4C4×C22⋊D4311yescharacteristic
329C2×C4M16×D4311yescharacteristic
330C2×C4#1306333111yescharacteristic
331C2×C4#1306333311yescharacteristic
332C8—41no—
333C8—862no—
334C8—1721no—
335C8#1306329711yescharacteristic
336C8#1306329811yescharacteristic
337C8#1306331111yescharacteristic
338C8#1306332111yescharacteristic
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—1722no—
348C22—1721no—
349C22#1458286111yescharacteristic
350C22#1458296711yescharacteristic
351C22#1458297011yescharacteristic
352C4—41no—
353C4—1722no—
354C4—1721no—
355C4#1458279911yescharacteristic
356C4#1458286411yescharacteristic
357C4#1458296811yescharacteristic
358C4#1458297311yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—3441no—
364C2#1913539111yescharacteristic
subgroupG/H
centerC8#13063321
commutatorC22×C4×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2112C2
socleC2×C43#1955
prime radical#14583410C4
cosocleC22×C8×C43C23
hypercenter#2112D43
hypocenterC43#13200
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
2. #19136360C2semidirect
3. #19136224C2semidirect
4. #19136222C2semidirect
5. #19136206C2semidirect
6. #19136199C2semidirect
7. C43×#2112C2semidirect
47. C2×C43⋊C16D4semidirect
67. C2×C16×C43D4semidirect
182. #2112D43semidirect
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
#191432892
#191363602
#191362242
#191362222
#191362062
#191361992
C43×#21122
#1320043