Finite Group Databasebeta

← #25014806

Subgroups — #25014806

Order 11008.

420 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143298C211yesmaximal, characteristic
2#19136360C211yesmaximal, characteristic, complemented
3#19136224C211yesmaximal, characteristic, complemented
4#19136222C211yesmaximal, characteristic, complemented
5C2×#14582681C211yesmaximal, characteristic, complemented
6#19136199C211yesmaximal, characteristic, complemented
7C2×C43×#349C211yesmaximal, characteristic, complemented
8C2×#13063331C2211yescharacteristic
9#14583410C411yescharacteristic
10C2×#13063265C2211yescharacteristic
11C2×#13063265C2211yescharacteristic
12#14582975—22no—
13#14582968—22no—
14#14582925C411yescharacteristic
15#14582865C411yescharacteristic
16#14582863C411yescharacteristic
17#14582854C2211yescharacteristic
18#14582719—22no—
19#14582684—22no—
20#14582682—22no—
21#14582681—22no—
22#14582676—22no—
23C22×M16×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C43×#349—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#13063265D412yescomplemented
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48Dic43⋊C8—22no—
49C22⋊(C43⋊C8)—22no—
50(C2×D43)⋊C8—22no—
51#13063235D412yes—
52C8×Dic43D412yes—
53C23×C4×C43C2×C411yescharacteristic
54C2×M16×C43—21no—
55C2×M16×C43—21no—
56C2×M16×C43—21no—
57C2×M16×C43—21no—
58C2×M16×C43—21no—
59C2×M16×C43—21no—
60C22×C8×C43C2×C411yescharacteristic
61C22×C8×C43C2311yescharacteristic
62M32×C43—21no—
63M32×C43—21no—
64M32×C43—21no—
65M32×C43D412yescomplemented
66C2×C16×C43—21no—
67C2×C16×C43—21no—
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
86M16×C43—41no—
87M16×C43—41no—
88M16×C43—41no—
89M16×C43—41no—
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
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—81no—
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—41no—
139C22⋊D43—41no—
140C22⋊D43—82no—
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#13201—431nomaximal, Sylow
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43#40711yescharacteristic
164C22×C43#43511yescharacteristic
165C22×C43#43511yescharacteristic
166C2×D43—42no—
167C2×D43—41no—
168C4×C43—41no—
169C4×C43#39011yescharacteristic
170C4×C43#40811yescharacteristic
171C4×C43#43511yescharacteristic
172C4×C43#43511yescharacteristic
173Dic43—42no—
174Dic43—41no—
175#2930—431no—
176#2153—431no—
177#2117—431no—
178#2117—431no—
179C2×#349—431no—
180C2×#349D4311yescharacteristic, complemented
181#2110—431no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—81no—
186C2×C43#195511yescharacteristic
187D43—81no—
188C2×#131—431no—
189C22×M16C2×D4311yescharacteristic
190#525—431no—
191C2×M32—431no—
192C2×M32—431no—
193C2×M32C2×D4311yescharacteristic
194C2×M32C2×D4311yescharacteristic
195#436—862no—
196#435—862no—
197#424—431no—
198#408—431no—
199#407—431no—
200#405—431no—
201#364—862no—
202#350—862no—
203#350—862no—
204#349—22no—
205#349—862no—
206#347—862no—
207C43#1320111yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C23×C4C4×D4311yescharacteristic
210#131—861no—
211#131—861no—
212#131—861no—
213#131—861no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—431no—
221C2×M16—431no—
222C2×M16—861no—
223C22×C8—861no—
224C22×C8C4×D4311yescharacteristic
225C22×C8C22×D4311yescharacteristic
226#123—861no—
227C22⋊Q8—861no—
228#121—861no—
229#120—861no—
230C4×D4—862no—
231#117—431no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32—432no—
236M32—861no—
237M32—861no—
238M32—861no—
239M32C22⋊D4312yescomplemented
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—861no—
243C2×C16—861no—
244C4⋊C8—862no—
245C22⋊C8—862no—
246C22⋊C8—862no—
247#97—432no—
248C4×C8—432no—
249C24#1062187211yescharacteristic
250#41—861no—
251#41—861no—
252#41—861no—
253#41—861no—
254C2×Q8—431no—
255C2×D4—431no—
256C2×D4—862no—
257C2×D4—861no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—861no—
265C22×C4#1062187211yescharacteristic
266C22×C4C2×C4×D4311yescharacteristic
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—861no—
272M16—861no—
273M16—861no—
274M16—861no—
275M16—1721no—
276M16—1721no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—432no—
281C2×C8—861no—
282C2×C8—1721no—
283C2×C8—1721no—
284C2×C8#1062189811yescharacteristic
285C2×C8D4×D4311yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8D4×D4311yescharacteristic
288C2×C8#1062190011yescharacteristic
289C2×C8C2×C22⋊D4311yescharacteristic
290C4⋊C4—862no—
291C4⋊C4—861no—
292C22⋊C4—862no—
293C22⋊C4—862no—
294C22⋊C4—861no—
295C42—432no—
296C16—22no—
297C16—41no—
298C16—862no—
299C16—1721no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—81no—
304C23—861no—
305C23C2×#1062187211yescharacteristic
306Q8—861no—
307Q8—861no—
308D4—861no—
309D4—861no—
310D4—3442no—
311D4—1721no—
312D4—1721no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—862no—
321C2×C4—861no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4C22⋊C4×D4311yescharacteristic
325C2×C4(C22⋊D43)⋊C411yescharacteristic
326C2×C4C4×C22⋊D4311yescharacteristic
327C2×C4M16×D4311yescharacteristic
328C2×C4#1306333111yescharacteristic
329C2×C4#1306333311yescharacteristic
330C8—41no—
331C8—862no—
332C8—1721no—
333C8#1306329711yescharacteristic
334C8#1306329811yescharacteristic
335C8#1306331111yescharacteristic
336C8#1306332111yescharacteristic
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22—1722no—
344C22—1721no—
345C22#1458286111yescharacteristic
346C22#1458296711yescharacteristic
347C22#1458297011yescharacteristic
348C4—41no—
349C4—1722no—
350C4—1721no—
351C4#1458279911yescharacteristic
352C4#1458286411yescharacteristic
353C4#1458296811yescharacteristic
354C4#1458297311yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—3441no—
360C2#1913539111yescharacteristic
subgroupG/H
centerC4#14582799
commutatorC22×C4×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#349C2
socleC2×C43#1955
prime radical#14583410C4
cosocleC22×C8×C43C23
hypercenterC2×#349D43
hypocenterC43#13201
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. #19136360C2semidirect
3. #19136224C2semidirect
4. #19136222C2semidirect
5. C2×#14582681C2semidirect
6. #19136199C2semidirect
7. C2×C43×#349C2semidirect
45. #13063265D4semidirect
65. M32×C43D4semidirect
180. C2×#349D43semidirect
207. C43#13201semidirect
239. M32C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191432982
#191363602
#191362242
#191362222
C2×#145826812
#191361992
C2×C43×#3492
#1320143