Finite Group Databasebeta

← #25014804

Subgroups — #25014804

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#19143296C211yesmaximal, characteristic
2#19136360C211yesmaximal, characteristic, complemented
3#19136223C211yesmaximal, characteristic, complemented
4C2×#14582680C211yesmaximal, characteristic, complemented
5C2×#14582680C211yesmaximal, characteristic, complemented
6#19136199C211yesmaximal, characteristic, complemented
7C43×#2117C211yesmaximal, characteristic, complemented
8C22×#10621872C2211yescharacteristic
9#14583406C411yescharacteristic
10C2×#13063265C2211yescharacteristic
11C2×#13063265C2211yescharacteristic
12#14582975—22no—
13#14582970—22no—
14#14582927C411yescharacteristic
15#14582866C411yescharacteristic
16#14582862C411yescharacteristic
17#14582854C2211yescharacteristic
18#14582719—22no—
19#14582683—22no—
20#14582680—22no—
21#14582680—22no—
22#14582676—22no—
23C2×#131×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C43×#350—22no—
27C22×C4×D43C2×C411yescharacteristic
28C2×#10621877C2×C411yescharacteristic
29C2×#10621872—21no—
30C2×#10621872—21no—
31C2×#10621872—21no—
32C2×#10621872—21no—
33C2×#10621872—21no—
34C2×#10621872—21no—
35C22×C43⋊C8C2×C411yescharacteristic
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#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—
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×C43D412yescomplemented
66C2×C16×C43—21no—
67C2×C16×C43—21no—
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—
111#10621872—41no—
112#10621872—41no—
113#10621872—41no—
114#10621872—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—81no—
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—82no—
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#13201—431nomaximal, Sylow
157C22×C43—41no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43#40711yescharacteristic
161C22×C43#43511yescharacteristic
162C22×C43#43511yescharacteristic
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—81no—
167C2×D43—81no—
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#2117D4311yescharacteristic, complemented
179C2×#349—431no—
180C2×#349—431no—
181#2110—431no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—81no—
186C2×C43#195511yescharacteristic
187D43—81no—
188C2×#131C2×D4311yescharacteristic
189C22×M16—431no—
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—22no—
203#350—862no—
204#349—862no—
205#349—862no—
206#347—862no—
207C43#1320111yescharacteristic, complemented, Sylow
208C2×#41C4×D4311yescharacteristic
209C23×C4—431no—
210#131—21no—
211#131—21no—
212#131—21no—
213#131—21no—
214C2×M16—21no—
215C2×M16—431no—
216C2×M16—861no—
217C2×M16—861no—
218C2×M16—861no—
219C2×M16—861no—
220C2×M16—861no—
221C2×M16—861no—
222C2×M16C4×D4311yescharacteristic
223C22×C8—21no—
224C22×C8—431no—
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—431no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—21no—
254C2×Q8#1062187211yescharacteristic
255C2×D4—21no—
256C2×D4—862no—
257C2×D4#1062187211yescharacteristic
258C22×C4—21no—
259C22×C4—431no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4C2×C4×D4311yescharacteristic
267M16—21no—
268M16—21no—
269M16—41no—
270M16—41no—
271M16—861no—
272M16—861no—
273M16—1721no—
274M16—1721no—
275M16—1721no—
276M16—1721no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—432no—
281C2×C8—861no—
282C2×C8—861no—
283C2×C8—861no—
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—861no—
302C23—861no—
303C23—861no—
304C23—3441no—
305C23M16×D4311yescharacteristic
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—3442no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—862no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4C22⋊C4×D4311yescharacteristic
325C2×C4(C22⋊D43)⋊C411yescharacteristic
326C2×C4C4×C22⋊D4311yescharacteristic
327C2×C4C2×#1062187211yescharacteristic
328C2×C4#1306333111yescharacteristic
329C2×C4#1306333311yescharacteristic
330C8—41no—
331C8—862no—
332C8—1721no—
333C8#1306329711yescharacteristic
334C8#1306329811yescharacteristic
335C8#1306331111yescharacteristic
336C8#1306332111yescharacteristic
337C22—41no—
338C22—42no—
339C22—41no—
340C22—3441no—
341C22—3441no—
342C22—1721no—
343C22—1721no—
344C22—1721no—
345C22#1458286111yescharacteristic
346C22#1458296811yescharacteristic
347C22#1458297311yescharacteristic
348C4—41no—
349C4—1722no—
350C4—1721no—
351C4#1458279911yescharacteristic
352C4#1458286411yescharacteristic
353C4#1458296711yescharacteristic
354C4#1458297011yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—3441no—
360C2#1913539111yescharacteristic
subgroupG/H
centerC4#14582799
commutatorC22×C4×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2117C2
socleC2×C43#1955
prime radical#14583406C4
cosocleC22×C8×C43C23
hypercenter#2117D43
hypocenterC43#13201
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. #19136360C2semidirect
3. #19136223C2semidirect
4. C2×#14582680C2semidirect
5. C2×#14582680C2semidirect
6. #19136199C2semidirect
7. C43×#2117C2semidirect
45. #13063265D4semidirect
65. M32×C43D4semidirect
178. #2117D43semidirect
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
#191432962
#191363602
#191362232
C2×#145826802
#191361992
C43×#21172
#1320143