Finite Group Databasebeta

← #25013717

Subgroups — #25013717

Order 11008.

462 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#19147729C211yesmaximal, characteristic
2C2×#14582705C211yesmaximal, characteristic, complemented
3#19136302C211yesmaximal, characteristic, complemented
4#19135493C211yesmaximal, characteristic, complemented
5#19132709C211yesmaximal, characteristic, complemented
6#19132684C211yesmaximal, characteristic, complemented
7C43×#2957C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583340—21no—
10#14583339C412yescomplemented
11#14583335—21no—
12#14583334C412yescomplemented
13#14583329—22no—
14C2×#13063265C2211yescharacteristic
15C22×C43⋊C16C2211yescharacteristic
16#14582937C2211yescharacteristic
17#14582915—21no—
18#14582872—21no—
19#14582705—22no—
20#14582703—21no—
21#14582700—21no—
22C2×#135×C43C2211yescharacteristic
23C43×#568—21no—
24C43×#444—22no—
25C43×#443—22no—
26C2×#108×C43C2211yescharacteristic
27C43×#421—21no—
28C43×#405C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347—21no—
33#13063347—21no—
34C2×Dic172C2×C411yescharacteristic
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic
37#13063284—21no—
38#13063271—22no—
39#13063269—22no—
40#13063268—22no—
41#13063266—22no—
42#13063265—21no—
43#13063265C2×C412yes—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48#13063259—21no—
49#13063257—21no—
50#13063251—42no—
51#13063239—42no—
52C2×#41×C43—21no—
53#135×C43—21no—
54#135×C43—21no—
55#135×C43C2×C412yes—
56#135×C43D412yes—
57C2×Q16×C43D411yescharacteristic
58C2×SD16×C43—21no—
59C2×D8×C43D411yescharacteristic
60#131×C43—24no—
61#131×C43—42no—
62C2×M16×C43—21no—
63C2×M16×C43—42no—
64C2×M16×C43D411yescharacteristic
65C22×C8×C43C2311yescharacteristic
66#117×C43D411yescharacteristic
67#108×C43—21no—
68#108×C43D412yes—
69#104×C43—24no—
70#97×C43—21no—
71C4×C8×C43—21no—
72#41×C43—22no—
73#41×C43—22no—
74#41×C43—41no—
75#41×C43—41no—
76C2×Q8×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81C2×C22⋊D43—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86C2×D172—21no—
87C2×C4×D43—41no—
88C2×Dic86—21no—
89Q16×C43—21no—
90Q16×C43C22⋊C412yes—
91SD16×C43—22no—
92SD16×C43—22no—
93D8×C43—21no—
94D8×C43C22⋊C412yes—
95M16×C43—21no—
96M16×C43—22no—
97M16×C43—44no—
98M16×C43—41no—
99M16×C43D812yes—
100C2×C8×C43—21no—
101C2×C8×C43—44no—
102C2×C8×C43—41no—
103C2×C8×C43C22×C411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C4⋊C4×C43—21no—
110C22⋊C4×C43—21no—
111C42×C43—21no—
112C22⋊Dic43—41no—
113C4⋊Dic43—41no—
114C4×Dic43—41no—
115Dic172—21no—
116Dic172—21no—
117D344—21no—
118D344—21no—
119#10621873—41no—
120#10621873—41no—
121C43⋊C16—22no—
122C43⋊C16—41no—
123C23×C43—41no—
124C23×C43AGL(1,ℤ/8)11yescharacteristic
125C22×D43—41no—
126Q8×C43—22no—
127Q8×C43—41no—
128D4×C43—22no—
129D4×C43—42no—
130D4×C43—42no—
131D4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43C2×D811yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—41no—
145C2×Dic43—81no—
146D172—41no—
147D172—41no—
148C4×D43—81no—
149C4×D43—81no—
150Dic86—41no—
151Dic86—41no—
152C8×C43—22no—
153C8×C43—42no—
154C8×C43C2×C22⋊C411yescharacteristic
155C8×C43C4×D411yescharacteristic
156C8×C43#12111yescharacteristic
157C8×C43#12311yescharacteristic
158#13021—431nomaximal, Sylow
159C22×C43—41no—
160C22×C43—42no—
161C22×C43—161no—
162C22×C43#44211yescharacteristic
163C22×C43#44911yescharacteristic
164C22×C43#45911yescharacteristic
165C2×D43—81no—
166C2×D43—161no—
167C4×C43—42no—
168C4×C43—81no—
169C4×C43#38611yescharacteristic
170C4×C43C4×D811yescharacteristic
171C4×C43#44711yescharacteristic
172C4×C43#46311yescharacteristic
173Dic43—81no—
174Dic43—161no—
175#3414—431no—
176#2957D4311yescharacteristic, complemented
177C2×#359—431no—
178#2138—431no—
179#1976—431no—
180#1389—431no—
181#1379—431no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—82no—
186C2×C43#187911yescharacteristic
187D43—161no—
188C2×#135—431no—
189C2×#135C2×D4311yescharacteristic
190#568—21no—
191#510—432no—
192#510—861no—
193#509—432no—
194#509—861no—
195#508—862no—
196C2×M32—431no—
197C22×C16—431no—
198#444—22no—
199#443—22no—
200C2×#108C2×D4311yescharacteristic
201#427—431no—
202#421—21no—
203#421—861no—
204#410—861no—
205#405C2×D4311yescharacteristic
206#359—862no—
207#358—861no—
208#357—861no—
209C43#1302111yescharacteristic, complemented, Sylow
210C2×#41—21no—
211C2×#41—861no—
212#135—21no—
213#135—21no—
214#135—861no—
215#135—861no—
216#135—861no—
217#135—861no—
218#135C4×D4312yes—
219#135C22⋊D4312yes—
220C2×Q16—431no—
221C2×Q16D17211yescharacteristic
222C2×SD16—21no—
223C2×SD16—861no—
224C2×D8—431no—
225C2×D8D17211yescharacteristic
226#131—24no—
227#131—42no—
228C2×M16—21no—
229C2×M16—42no—
230C2×M16C22⋊D4311yescharacteristic
231C22×C8C22×D4311yescharacteristic
232#117—861no—
233#117C22⋊D4311yescharacteristic
234Q32—862no—
235SD32—862no—
236SD32—862no—
237D16—862no—
238M32—432no—
239M32—861no—
240C2×C16—861no—
241C2×C16—861no—
242C2×C16—861no—
243C2×C16—861no—
244#108—21no—
245#108C22⋊D4312yes—
246#107—861no—
247#106—861no—
248#104—24no—
249#104—1722no—
250#99—1722no—
251#97—21no—
252C4×C8—21no—
253#41—22no—
254#41—22no—
255#41—41no—
256#41—41no—
257#41—1721no—
258#41—1721no—
259#41—1721no—
260#41—1721no—
261C2×Q8—21no—
262C2×Q8—861no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—861no—
266C2×D4—1721no—
267C22×C4—41no—
268C22×C4—1721no—
269C22×C4C2×C22⋊D4311yescharacteristic
270Q16—21no—
271Q16—861no—
272Q16—861no—
273Q16(C2×D43)⋊C412yes—
274SD16—22no—
275SD16—22no—
276SD16—1721no—
277SD16—1721no—
278D8—21no—
279D8—861no—
280D8—861no—
281D8(C2×D43)⋊C412yes—
282M16—21no—
283M16—22no—
284M16—44no—
285M16—41no—
286M16#1062188212yes—
287C2×C8—21no—
288C2×C8—44no—
289C2×C8—41no—
290C2×C8C2×C4×D4311yescharacteristic
291C2×C8C2×D17211yescharacteristic
292C2×C8#1062189811yescharacteristic
293C2×C8#1062189811yescharacteristic
294C2×C8C2×C22⋊D4311yescharacteristic
295C2×C8C2×C22⋊D4311yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—1721no—
298C22⋊C4—21no—
299C22⋊C4—1721no—
300C42—21no—
301C42—1721no—
302C16—862no—
303C16—1721no—
304C23—41no—
305C23—1721no—
306C23#1306335011yescharacteristic
307Q8—22no—
308Q8—41no—
309Q8—1721no—
310Q8—1721no—
311D4—22no—
312D4—42no—
313D4—42no—
314D4—41no—
315D4—3441no—
316D4—3441no—
317D4—1721no—
318D4—1721no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—3441no—
324C2×C4—3441no—
325C2×C4—3441no—
326C2×C4—1721no—
327C2×C4C4×C22⋊D4311yescharacteristic
328C2×C4#1306329411yescharacteristic
329C2×C4#1306329911yescharacteristic
330C2×C4C2×#1062188211yescharacteristic
331C2×C4#1306334511yescharacteristic
332C2×C4#1306335111yescharacteristic
333C8—22no—
334C8—42no—
335C8C2×(C2×D43)⋊C411yescharacteristic
336C8C4×C22⋊D4311yescharacteristic
337C8#1306329911yescharacteristic
338C8#1306330811yescharacteristic
339C22—41no—
340C22—42no—
341C22—161no—
342C22—3441no—
343C22—6881no—
344C22#1458300911yescharacteristic
345C22#1458304411yescharacteristic
346C22#1458309411yescharacteristic
347C4—42no—
348C4—81no—
349C4—3441no—
350C4—6881no—
351C4#1458277811yescharacteristic
352C4C4×#1062188211yescharacteristic
353C4#1458303311yescharacteristic
354C4#1458311411yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—82no—
359C2—6881no—
360C2#1913494311yescharacteristic
subgroupG/H
centerC4#14583033
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2957C2
socleC2×C43#1879
prime radical#19147729C2
cosocleC22×C8×C43C23
hypercenter#2957D43
hypocenterC43#13021
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. C2×#14582705C2semidirect
3. #19136302C2semidirect
4. #19135493C2semidirect
5. #19132709C2semidirect
6. #19132684C2semidirect
7. C43×#2957C2semidirect
10. #14583339C4semidirect
12. #14583334C4semidirect
176. #2957D43semidirect
209. C43#13021semidirect

Maximal subgroups

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

subgroupindex
#191477292
C2×#145827052
#191363022
#191354932
#191327092
#191326842
C43×#29572
#1302143