Finite Group Databasebeta

← #25013682

Subgroups — #25013682

Order 11008.

462 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
1C2×#14583329C211yesmaximal, characteristic
2#19136331C211yesmaximal, characteristic, complemented
3#19136322C211yesmaximal, characteristic, complemented
4#19135493C211yesmaximal, characteristic, complemented
5#19132692C211yesmaximal, characteristic, complemented
6#19132684C211yesmaximal, characteristic, complemented
7C43×#2957C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583329—22no—
10#14583329—22no—
11C2×#13063271C411yescharacteristic, complemented
12C2×#13063269C411yescharacteristic, complemented
13C2×#13063268C411yescharacteristic, complemented
14C2×#13063266C411yescharacteristic, complemented
15C2×#13063265C2211yescharacteristic
16C22×C43⋊C16C2211yescharacteristic
17#14582937C2211yescharacteristic
18#14582915—21no—
19#14582872—21no—
20#14582709—22no—
21#14582705—22no—
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#13063265—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16C2×C411yescharacteristic
48C2×C43⋊C16C2×C411yescharacteristic
49#13063259—21no—
50#13063257—21no—
51#13063251—42no—
52#13063239—42no—
53C2×#41×C43—21no—
54#135×C43—21no—
55#135×C43—21no—
56#135×C43D412yes—
57#135×C43D412yes—
58C2×Q16×C43C2×C411yescharacteristic
59C2×SD16×C43—21no—
60C2×D8×C43C2×C411yescharacteristic
61#131×C43—24no—
62#131×C43—42no—
63C2×M16×C43—21no—
64C2×M16×C43—42no—
65C2×M16×C43D411yescharacteristic
66C22×C8×C43C2311yescharacteristic
67#117×C43D411yescharacteristic
68#108×C43—21no—
69#108×C43D412yes—
70#104×C43—24no—
71#97×C43—21no—
72C4×C8×C43—21no—
73#41×C43—22no—
74#41×C43—22no—
75#41×C43—41no—
76#41×C43—41no—
77C2×Q8×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43C2×D411yescharacteristic
82C2×C22⋊D43—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87C2×D172—21no—
88C2×C4×D43—41no—
89C2×Dic86—21no—
90Q16×C43—21no—
91Q16×C43C22⋊C412yes—
92SD16×C43—22no—
93SD16×C43—22no—
94D8×C43—21no—
95D8×C43C22⋊C412yes—
96M16×C43—21no—
97M16×C43—22no—
98M16×C43—44no—
99M16×C43—41no—
100M16×C43D812yes—
101C2×C8×C43—21no—
102C2×C8×C43—44no—
103C2×C8×C43—41no—
104C2×C8×C43C22×C411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C2×C8×C43#4111yescharacteristic
110C4⋊C4×C43—21no—
111C22⋊C4×C43—21no—
112C42×C43—21no—
113C22⋊Dic43—41no—
114C4⋊Dic43—41no—
115C4×Dic43—41no—
116Dic172—21no—
117Dic172—21no—
118D344—21no—
119D344—21no—
120#10621873—41no—
121#10621873—41no—
122C43⋊C16—21no—
123C43⋊C16—21no—
124C43⋊C16—41no—
125C23×C43—41no—
126C23×C43AGL(1,ℤ/8)11yescharacteristic
127C22×D43—41no—
128Q8×C43—22no—
129Q8×C43—41no—
130D4×C43—22no—
131D4×C43—42no—
132D4×C43—42no—
133D4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—41no—
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43C2×D811yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C22⋊D43—81no—
145C22⋊D43—81no—
146C2×Dic43—41no—
147C2×Dic43—81no—
148D172—41no—
149D172—41no—
150C4×D43—81no—
151C4×D43—81no—
152Dic86—41no—
153Dic86—41no—
154C8×C43—22no—
155C8×C43—42no—
156C8×C43C2×C22⋊C411yescharacteristic
157C8×C43C4×D411yescharacteristic
158C8×C43#12111yescharacteristic
159C8×C43#12311yescharacteristic
160#13016—431nomaximal, Sylow
161C22×C43—41no—
162C22×C43—42no—
163C22×C43—161no—
164C22×C43#44211yescharacteristic
165C22×C43#44911yescharacteristic
166C22×C43#45911yescharacteristic
167C2×D43—81no—
168C2×D43—161no—
169C4×C43—42no—
170C4×C43—81no—
171C4×C43#38611yescharacteristic
172C4×C43C4×D811yescharacteristic
173C4×C43#44711yescharacteristic
174C4×C43#46311yescharacteristic
175Dic43—81no—
176Dic43—161no—
177C2×#508—431no—
178#2957D4311yescharacteristic, complemented
179#2145—431no—
180#2143—431no—
181#1976—431no—
182#1382—431no—
183#1379—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—82no—
188C2×C43#187911yescharacteristic
189D43—161no—
190C2×#135—431no—
191C2×#135C2×D4311yescharacteristic
192#568—21no—
193#508—862no—
194#508—862no—
195C2×Q32—431no—
196C2×SD32—431no—
197C2×SD32—431no—
198C2×D16—431no—
199C2×M32—431no—
200C22×C16—431no—
201#444—22no—
202#443—22no—
203C2×#108C2×D4311yescharacteristic
204#427—431no—
205#421—21no—
206#421—861no—
207#410—861no—
208#405C2×D4311yescharacteristic
209#360—862no—
210#359—862no—
211C43#1301611yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C2×#41—861no—
214#135—21no—
215#135—21no—
216#135—861no—
217#135—861no—
218#135—861no—
219#135—861no—
220#135D17212yes—
221#135C22⋊D4312yes—
222C2×Q16—431no—
223C2×Q16C4×D4311yescharacteristic
224C2×SD16—21no—
225C2×SD16—861no—
226C2×D8—431no—
227C2×D8C4×D4311yescharacteristic
228#131—24no—
229#131—42no—
230C2×M16—21no—
231C2×M16—42no—
232C2×M16C22⋊D4311yescharacteristic
233C22×C8C22×D4311yescharacteristic
234#117—861no—
235#117C22⋊D4311yescharacteristic
236Q32—862no—
237SD32—862no—
238SD32—862no—
239D16—862no—
240M32—861no—
241M32—861no—
242C2×C16—431no—
243C2×C16—431no—
244C2×C16—861no—
245C2×C16—861no—
246C2×C16—861no—
247#108—21no—
248#108C22⋊D4312yes—
249#107—861no—
250#106—861no—
251#104—24no—
252#104—1722no—
253#99—1722no—
254#97—21no—
255C4×C8—21no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260#41—1721no—
261#41—1721no—
262#41—1721no—
263#41—1721no—
264C2×Q8—21no—
265C2×Q8—861no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—861no—
269C2×D4—1721no—
270C22×C4—41no—
271C22×C4—1721no—
272C22×C4C2×C22⋊D4311yescharacteristic
273Q16—21no—
274Q16—861no—
275Q16—861no—
276Q16(C2×D43)⋊C412yes—
277SD16—22no—
278SD16—22no—
279SD16—1721no—
280SD16—1721no—
281D8—21no—
282D8—861no—
283D8—861no—
284D8(C2×D43)⋊C412yes—
285M16—21no—
286M16—22no—
287M16—44no—
288M16—41no—
289M16#1062188212yes—
290C2×C8—21no—
291C2×C8—44no—
292C2×C8—41no—
293C2×C8C2×C4×D4311yescharacteristic
294C2×C8C2×D17211yescharacteristic
295C2×C8#1062189811yescharacteristic
296C2×C8#1062189811yescharacteristic
297C2×C8C2×C22⋊D4311yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—1721no—
301C22⋊C4—21no—
302C22⋊C4—1721no—
303C42—21no—
304C42—1721no—
305C16—861no—
306C16—861no—
307C16—1721no—
308C23—41no—
309C23—1721no—
310C23#1306335011yescharacteristic
311Q8—22no—
312Q8—41no—
313Q8—1721no—
314Q8—1721no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—3441no—
320D4—3441no—
321D4—1721no—
322D4—1721no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—3441no—
330C2×C4—1721no—
331C2×C4C4×C22⋊D4311yescharacteristic
332C2×C4#1306329411yescharacteristic
333C2×C4#1306329911yescharacteristic
334C2×C4C2×#1062188211yescharacteristic
335C2×C4#1306334511yescharacteristic
336C2×C4#1306335111yescharacteristic
337C8—22no—
338C8—42no—
339C8C2×(C2×D43)⋊C411yescharacteristic
340C8C4×C22⋊D4311yescharacteristic
341C8#1306329911yescharacteristic
342C8#1306330811yescharacteristic
343C22—41no—
344C22—42no—
345C22—161no—
346C22—3441no—
347C22—6881no—
348C22#1458300911yescharacteristic
349C22#1458304411yescharacteristic
350C22#1458309411yescharacteristic
351C4—42no—
352C4—81no—
353C4—3441no—
354C4—6881no—
355C4#1458277811yescharacteristic
356C4C4×#1062188211yescharacteristic
357C4#1458303311yescharacteristic
358C4#1458311411yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—6881no—
364C2#1913494311yescharacteristic
subgroupG/H
centerC4#14583033
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2957C2
socleC2×C43#1879
prime radicalC2×#14583329C2
cosocleC22×C8×C43C23
hypercenter#2957D43
hypocenterC43#13016
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. #19136331C2semidirect
3. #19136322C2semidirect
4. #19135493C2semidirect
5. #19132692C2semidirect
6. #19132684C2semidirect
7. C43×#2957C2semidirect
11. C2×#13063271C4semidirect
12. C2×#13063269C4semidirect
13. C2×#13063268C4semidirect
14. C2×#13063266C4semidirect
178. #2957D43semidirect
211. C43#13016semidirect

Maximal subgroups

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

subgroupindex
C2×#145833292
#191363312
#191363222
#191354932
#191326922
#191326842
C43×#29572
#1301643