Finite Group Databasebeta

← #25014422

Subgroups — #25014422

Order 11008.

324 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582728C211yesmaximal, characteristic, complemented
2C2×#14582705C211yesmaximal, characteristic
3#19136300C211yesmaximal, characteristic
4#19135483C211yesmaximal, characteristic
5#19132690C211yesmaximal, characteristic, complemented
6#19132673C211yesmaximal, characteristic, complemented
7C43×#1772C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C22×C43⋊C16C2211yescharacteristic
10C22×C43⋊C16C2211yescharacteristic
11C2×#13063261C2211yescharacteristic
12C2×#13063253—21no—
13#14582865—21no—
14#14582728—22no—
15#14582705—22no—
16#14582702C411yescharacteristic, complemented
17#14582702C411yescharacteristic, complemented
18#14582699C411yescharacteristic, complemented
19#14582699C411yescharacteristic, complemented
20C2×#108×C43C2211yescharacteristic
21C43×#427C2211yescharacteristic
22C43×#405—21no—
23C2×C4×C8×C43C2211yescharacteristic
24C43×#339—21no—
25C2×#10621898—21no—
26#13063347—21no—
27#13063347—21no—
28#13063347—21no—
29#13063347—21no—
30C2×Dic172C2×C411yescharacteristic
31C2×#10621873—21no—
32C2×D344C2×C411yescharacteristic
33C2×#10621877—21no—
34C2×C43⋊C16—21no—
35C2×C43⋊C16—21no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16—21no—
39C2×C43⋊C16C2×C411yescharacteristic
40C2×C43⋊C16C2×C411yescharacteristic
41#13063261—21no—
42#13063261—21no—
43#13063253—42no—
44(C2×D43)⋊C8—41no—
45(C2×D43)⋊C8—41no—
46C2×M16×C43—21no—
47C22×C8×C43D411yescharacteristic
48C22×C8×C43C2311yescharacteristic
49#117×C43—21no—
50C2×C42×C43D411yescharacteristic
51#108×C43—21no—
52#108×C43D412yes—
53#107×C43C2×C411yescharacteristic
54#107×C43C2×C411yescharacteristic
55#106×C43—21no—
56#97×C43—41no—
57C4×C8×C43—21no—
58C4×C8×C43—21no—
59C4×C8×C43—41no—
60C22×C4×C43—21no—
61C22×C4×C43C2×D411yescharacteristic
62C2×C22⋊D43—41no—
63#10621898—41no—
64#10621898—41no—
65#10621898—41no—
66#10621898—41no—
67C2×D172—21no—
68C2×C4×D43—41no—
69C2×Dic86—21no—
70M16×C43—22no—
71M16×C43—41no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43—41no—
75C2×C8×C43D811yescharacteristic
76C2×C8×C43D811yescharacteristic
77C2×C8×C43C22×C411yescharacteristic
78C2×C8×C43C2×D411yescharacteristic
79C2×C8×C43#4111yescharacteristic
80C2×C8×C43#4111yescharacteristic
81C2×C8×C43#4111yescharacteristic
82C2×C8×C43#4111yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C22⋊C4×C43—41no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—41no—
89#10621877—41no—
90#10621877—41no—
91C2×C43⋊C8—41no—
92Dic172—21no—
93Dic172—21no—
94D344—21no—
95D344—21no—
96#10621873—41no—
97#10621873—41no—
98C43⋊C16—21no—
99C43⋊C16—21no—
100C43⋊C16—41no—
101C23×C43#13511yescharacteristic
102C22×D43—41no—
103C2×C4×C43—22no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43C4×D411yescharacteristic
109C2×C4×C43#12111yescharacteristic
110C2×C4×C43#12311yescharacteristic
111C2×C4×C43C2×D811yescharacteristic
112C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C43#13711yescharacteristic
114C22⋊D43—81no—
115C22⋊D43—81no—
116C2×Dic43—41no—
117D172—41no—
118D172—41no—
119C4×D43—81no—
120C4×D43—81no—
121Dic86—41no—
122Dic86—41no—
123C8×C43—21no—
124C8×C43—21no—
125C8×C43—42no—
126C8×C43#11711yescharacteristic
127C8×C43C4×D411yescharacteristic
128C8×C43#12411yescharacteristic
129C8×C43#12611yescharacteristic
130C43⋊C8—81no—
131#13134—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43C4×D811yescharacteristic
135C22×C43#46411yescharacteristic
136C22×C43#48211yescharacteristic
137C2×D43—81no—
138C2×D43—81no—
139C2×D43—81no—
140C4×C43—42no—
141C4×C43—81no—
142C4×C43—81no—
143C4×C43#38811yescharacteristic
144C4×C43#44011yescharacteristic
145C4×C43#45911yescharacteristic
146C4×C43#48011yescharacteristic
147Dic43—81no—
148C2×#368—431no—
149C2×#359—431no—
150#2138—431no—
151#1974—431no—
152#1772D4311yescharacteristic, complemented
153#1382—431no—
154#1374—431no—
155C2×C43—21no—
156C2×C43—21no—
157C2×C43#192511yescharacteristic
158C2×C43#217811yescharacteristic
159C2×C43#217911yescharacteristic
160D43—161no—
161C2×#135—431no—
162C22×C16—431no—
163C22×C16—431no—
164C2×#108—431no—
165C2×#108C2×D4311yescharacteristic
166#427C2×D4311yescharacteristic
167C2×#104—861no—
168#408—861no—
169#405—21no—
170C2×C4×C8C2×D4311yescharacteristic
171#368—862no—
172#359—862no—
173#358—431no—
174#358—431no—
175#357—431no—
176#357—431no—
177#339—21no—
178C43#1313411yescharacteristic, complemented, Sylow
179C2×#41—861no—
180#135—861no—
181#135—861no—
182#135—861no—
183#135—861no—
184C2×Q16—431no—
185C2×SD16—861no—
186C2×D8—431no—
187C2×M16—21no—
188C2×M16—861no—
189C22×C8C22⋊D4311yescharacteristic
190C22×C8C22×D4311yescharacteristic
191#117—21no—
192C2×C42C22⋊D4311yescharacteristic
193C2×C16—431no—
194C2×C16—431no—
195C2×C16—861no—
196C2×C16—861no—
197C2×C16—861no—
198C2×C16—861no—
199C2×C16—861no—
200#108—21no—
201#108—861no—
202#108—861no—
203#108D17212yes—
204#107C4×D4311yescharacteristic
205#107C4×D4311yescharacteristic
206#106—21no—
207#104—1722no—
208C22⋊C8—1721no—
209C22⋊C8—1721no—
210#97—41no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—41no—
214#41—1721no—
215#41—1721no—
216#41—1721no—
217#41—1721no—
218C2×Q8—861no—
219C2×D4—861no—
220C2×D4—1721no—
221C22×C4—21no—
222C22×C4—1721no—
223C22×C4C2×C22⋊D4311yescharacteristic
224Q16—861no—
225Q16—861no—
226SD16—1721no—
227SD16—1721no—
228D8—861no—
229D8—861no—
230M16—22no—
231M16—41no—
232M16—1721no—
233M16—1721no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—1721no—
238C2×C8#1062188211yescharacteristic
239C2×C8#1062188211yescharacteristic
240C2×C8C2×C4×D4311yescharacteristic
241C2×C8C2×D17211yescharacteristic
242C2×C8#1062189811yescharacteristic
243C2×C8#1062189811yescharacteristic
244C2×C8#1062189811yescharacteristic
245C2×C8#1062189811yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C22⋊C4—41no—
249C42—21no—
250C42—21no—
251C42—41no—
252C16—861no—
253C16—861no—
254C16—1721no—
255C23—1721no—
256C23#1306334511yescharacteristic
257Q8—1721no—
258Q8—1721no—
259D4—3441no—
260D4—3441no—
261D4—1721no—
262D4—1721no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—3441no—
269C2×C4—3441no—
270C2×C4—1721no—
271C2×C4C4×C22⋊D4311yescharacteristic
272C2×C4#1306329911yescharacteristic
273C2×C4#1306330811yescharacteristic
274C2×C4C2×#1062188211yescharacteristic
275C2×C4#1306335011yescharacteristic
276C2×C4#1306335611yescharacteristic
277C8—21no—
278C8—21no—
279C8—42no—
280C8—3441no—
281C8#1306328211yescharacteristic
282C8C4×D17211yescharacteristic
283C8#1306331311yescharacteristic
284C8#1306331911yescharacteristic
285C22—21no—
286C22—21no—
287C22—3441no—
288C22—3441no—
289C22—3441no—
290C22C4×#1062188211yescharacteristic
291C22#1458312111yescharacteristic
292C22#1458322311yescharacteristic
293C4—42no—
294C4—81no—
295C4—81no—
296C4—3441no—
297C4#1458279011yescharacteristic
298C4#1458299711yescharacteristic
299C4#1458309411yescharacteristic
300C4#1458321211yescharacteristic
301C2—21no—
302C2—21no—
303C2—6881no—
304C2#1913521511yescharacteristic
305C2#1913647411yescharacteristic
306C2#1913647911yescharacteristic
subgroupG/H
centerC2×C4C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1772C2
socleC22×C43C4×D8
prime radicalC2×#13063347C22
cosocleC22×C8×C43C23
hypercenter#1772D43
hypocenterC43#13134
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1772

Complements

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

NH ≅ G/Ntype
1. C2×#14582728C2semidirect
5. #19132690C2semidirect
6. #19132673C2semidirect
7. C43×#1772C2semidirect
16. #14582702C4semidirect
17. #14582702C4semidirect
18. #14582699C4semidirect
19. #14582699C4semidirect
152. #1772D43semidirect
178. C43#13134semidirect

Maximal subgroups

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

subgroupindex
C2×#145827282
C2×#145827052
#191363002
#191354832
#191326902
#191326732
C43×#17722
#1313443