Finite Group Databasebeta

← #24993254

Subgroups — #24993254

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145517C211yesmaximal, characteristic
2#19135568C211yesmaximal, characteristic, complemented
3#19133281C211yesmaximal, characteristic, complemented
4#19133155C211yesmaximal, characteristic
5#19132455C211yesmaximal, characteristic, complemented
6#19132426C211yesmaximal, characteristic, complemented
7C43×#2932C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583271C412yescomplemented
10#14583251C412yescomplemented
11#14583104—22no—
12#14583037—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582765C2211yescharacteristic
16#14582662—21no—
17#14582662—21no—
18#14582644—22no—
19#14582633—22no—
20C2×#131×C43—21no—
21C43×#532C2211yescharacteristic
22C43×#435—22no—
23C43×#435—22no—
24C43×#423C2211yescharacteristic
25C43×#408—21no—
26C2×#97×C43C2211yescharacteristic
27C22×Dic86—21no—
28C2×#10621883—24no—
29#13063325—21no—
30#13063325—21no—
31#13063325—21no—
32#13063325C2×C412yes—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38#13063248—24no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8C2×C412yes—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C2×#41×C43—21no—
46#131×C43—42no—
47#131×C43—42no—
48C2×M16×C43—22no—
49C2×M16×C43—21no—
50C22×C8×C43—22no—
51C22×C8×C43D411yescharacteristic
52C22×C8×C43D411yescharacteristic
53C4⋊Q8×C43C2×C411yescharacteristic
54#127×C43C2×C411yescharacteristic
55#124×C43—21no—
56#121×C43—21no—
57#121×C43D412yes—
58C4×D4×C43—21no—
59C4×D4×C43D412yes—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43D412yes—
63C22⋊C8×C43—24no—
64#97×C43—21no—
65#97×C43—21no—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69#41×C43—41no—
70C2×Q8×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—22no—
74C2×D4×C43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—41no—
80C22×Dic43—41no—
81C2×Dic86—22no—
82C2×Dic86—41no—
83C2×Dic86—82no—
84M16×C43—44no—
85M16×C43—41no—
86M16×C43—41no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—22no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—44no—
94C2×C8×C43SD1612yescomplemented
95C4⋊C4×C43—21no—
96C4⋊C4×C43C22⋊C412yes—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103#10621883—84no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—41no—
112C23×C43—22no—
113C23×C43#12111yescharacteristic
114Q8×C43—41no—
115Q8×C43—41no—
116D4×C43—42no—
117D4×C43—42no—
118D4×C43—42no—
119D4×C43—41no—
120D4×C43—41no—
121D4×C43—81no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43C2×C22⋊C411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12311yescharacteristic
133C2×C4×C43C2×SD1611yescharacteristic
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43#13711yescharacteristic
137C2×Dic43—42no—
138C2×Dic43—82no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142Dic86—44no—
143Dic86—82no—
144C8×C43—22no—
145C8×C43—42no—
146C8×C43—41no—
147C43⋊C8—42no—
148C43⋊C8—81no—
149#9289—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43#38611yescharacteristic
156C22×C43#46111yescharacteristic
157C22×C43#46311yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—42no—
163C4×C43C4×SD1611yescharacteristic
164C4×C43#44011yescharacteristic
165C4×C43#45011yescharacteristic
166C4×C43#45211yescharacteristic
167Dic43—82no—
168Dic43—161no—
169#3206—431no—
170#2932D4311yescharacteristic
171#1993—431no—
172#1549—431no—
173#1517—431no—
174#1286—431no—
175#1275—431no—
176C2×C43—21no—
177C2×C43—21no—
178C2×C43—82no—
179C2×C43#187711yescharacteristic
180C2×C43#190211yescharacteristic
181C2×C43#191011yescharacteristic
182C2×#131—21no—
183#532C2×D4311yescharacteristic
184C2×C4⋊Q8—431no—
185#492—432no—
186#487—432no—
187#461—862no—
188#448—862no—
189#435—22no—
190#435—22no—
191#431—431no—
192#431—431no—
193#423C2×D4311yescharacteristic
194#408—21no—
195C2×#97C2×D4311yescharacteristic
196#382—431no—
197#340—861no—
198#340—861no—
199#332—862no—
200#327—862no—
201C43#928911yescharacteristic, complemented, Sylow
202C2×#41—21no—
203C22×Q8—861no—
204C2×SD16—864no—
205#131—42no—
206#131—42no—
207C2×M16—22no—
208C2×M16—21no—
209C22×C8—22no—
210C22×C8C22⋊D4311yescharacteristic
211C22×C8C22⋊D4311yescharacteristic
212C4⋊Q8—432no—
213C4⋊Q8—861no—
214C4⋊Q8—861no—
215C4⋊Q8—861no—
216C4⋊Q8C4×D4311yescharacteristic
217#127C4×D4311yescharacteristic
218#124—21no—
219#121—21no—
220#121D17212yes—
221C4×D4—21no—
222C4×D4C22⋊D4312yes—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—861no—
229C4⋊C8—861no—
230C4⋊C8C22⋊D4312yes—
231#103—864no—
232C22⋊C8—24no—
233C22⋊C8—861no—
234C22⋊C8—861no—
235#97—21no—
236#97—21no—
237C4×C8—432no—
238C4×C8—861no—
239#95—861no—
240#95—861no—
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—862no—
247C2×Q8—3442no—
248C2×Q8—1721no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4(C2×D43)⋊C412yes—
253C22×C4—22no—
254C22×C4—1721no—
255C22×C4—1721no—
256C22×C4C2×D17211yescharacteristic
257C22×C4#1062189811yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259SD16—3444no—
260M16—44no—
261M16—41no—
262M16—41no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—22no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—44no—
270C2×C8—862no—
271C2×C8—1721no—
272C2×C8#1062188312yescomplemented
273C4⋊C4—21no—
274C4⋊C4—862no—
275C4⋊C4—862no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4(C2×D43)⋊C412yes—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C42C2×C4×D4311yescharacteristic
284C42#1062189811yescharacteristic
285C42C2×C22⋊D4311yescharacteristic
286C42C2×C22⋊D4311yescharacteristic
287C23—22no—
288C23#1306329911yescharacteristic
289Q8—41no—
290Q8—41no—
291Q8—3442no—
292Q8—1724no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—81no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—3442no—
305C2×C4—3441no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—1722no—
309C2×C4C2×(C2×D43)⋊C411yescharacteristic
310C2×C4C4×C22⋊D4311yescharacteristic
311C2×C4C4×C22⋊D4311yescharacteristic
312C2×C4#1306329411yescharacteristic
313C2×C4#1306329911yescharacteristic
314C2×C4#1306330811yescharacteristic
315C2×C4C2×#1062188311yescharacteristic
316C2×C4#1306334511yescharacteristic
317C2×C4#1306335111yescharacteristic
318C2×C4#1306335511yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—3441no—
323C8—1722no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22#1458277811yescharacteristic
330C22#1458310411yescharacteristic
331C22#1458311411yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—3442no—
338C4—6881no—
339C4C4×#1062188311yescharacteristic
340C4#1458299911yescharacteristic
341C4#1458305011yescharacteristic
342C4#1458306111yescharacteristic
343C2—21no—
344C2—21no—
345C2—82no—
346C2#1913492911yescharacteristic
347C2#1913506811yescharacteristic
348C2#1913512211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2932C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2932D43
hypocenterC43#9289
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #19135568C2semidirect
3. #19133281C2semidirect
5. #19132455C2semidirect
6. #19132426C2semidirect
9. #14583271C4semidirect
10. #14583251C4semidirect
94. C2×C8×C43SD16semidirect
201. C43#9289semidirect
272. C2×C8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191455172
#191355682
#191332812
#191331552
#191324552
#191324262
C43×#29322
#928943