Finite Group Databasebeta

← #25014037

Subgroups — #25014037

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583316C211yesmaximal, characteristic, complemented
2C2×#14583169C211yesmaximal, characteristic
3C2×#14582711C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5#19132703C211yesmaximal, characteristic, complemented
6#19132688C211yesmaximal, characteristic, complemented
7C43×#1816C211yesmaximal, characteristic, complemented
8C2×#13063350—21no—
9C22×D344C2211yescharacteristic
10#14583316—22no—
11#14583316—22no—
12C2×#13063265—21no—
13C2×#13063265C2211yescharacteristic
14C22×C43⋊C16—21no—
15C22×C43⋊C16C2211yescharacteristic
16#14583169—22no—
17#14583169C414yescomplemented
18C2×#13063261C2211yescharacteristic
19C2×#13063241—21no—
20#14582711—22no—
21#14582699—21no—
22#14582699—21no—
23C2×#131×C43C2211yescharacteristic
24C2×#108×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C43×#417—21no—
27C43×#343—21no—
28C22×D172—21no—
29#13063350—24no—
30#13063350—42no—
31C2×#10621884—41no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344—21no—
36C2×D344—21no—
37C2×D344C2×C412yes—
38C2×#10621882—41no—
39C2×#10621877—21no—
40#13063265—24no—
41#13063265—21no—
42#13063265D412yes—
43C2×C43⋊C16—24no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16D411yescharacteristic
48C2×C43⋊C16D411yescharacteristic
49#13063261—21no—
50#13063261C2×C412yes—
51#13063241—24no—
52C2×#41×C43D411yescharacteristic
53#131×C43—21no—
54#131×C43—21no—
55#131×C43C2×C412yes—
56#131×C43D412yes—
57C2×M16×C43—21no—
58C2×M16×C43—21no—
59C2×M16×C43D411yescharacteristic
60C22×C8×C43—21no—
61C22×C8×C43C2311yescharacteristic
62C2×C4⋊C4×C43—21no—
63#108×C43—21no—
64#108×C43—21no—
65#107×C43—21no—
66#107×C43—21no—
67#103×C43—41no—
68#102×C43—41no—
69C23×D43—41no—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43C22⋊C412yes—
73#41×C43SD1612yes—
74C2×Q8×C43D811yescharacteristic
75C2×D4×C43—21no—
76C2×D4×C43D811yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C2×D172—22no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86M16×C43—21no—
87M16×C43—22no—
88M16×C43—22no—
89M16×C43—41no—
90M16×C43—41no—
91M16×C43C22⋊C412yes—
92C2×C8×C43—21no—
93C2×C8×C43—22no—
94C2×C8×C43—22no—
95C2×C8×C43—41no—
96C2×C8×C43C22×C411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104#10621884—44no—
105#10621882—44no—
106#10621877—22no—
107#10621877—41no—
108C2×C43⋊C8—41no—
109D344—22no—
110D344—22no—
111D344—41no—
112D344—41no—
113C43⋊C16—21no—
114C43⋊C16—22no—
115C43⋊C16—21no—
116C23×C43—21no—
117C23×C43#13511yescharacteristic
118C22×D43—42no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43—161no—
122C22×D43—161no—
123Q8×C43—21no—
124Q8×C43#10212yes—
125D4×C43—22no—
126D4×C43—22no—
127D4×C43—21no—
128D4×C43#10212yes—
129C2×C4×C43—21no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—81no—
133C2×C4×C43—161no—
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43C2×D811yescharacteristic
138C2×C4×C43C2×SD1611yescharacteristic
139C2×C4×C43#13511yescharacteristic
140D172—42no—
141D172—42no—
142D172—81no—
143D172—81no—
144C8×C43—22no—
145C8×C43—81no—
146C8×C43C4×D411yescharacteristic
147C8×C43C4×D411yescharacteristic
148C8×C43#12011yescharacteristic
149C8×C43#12311yescharacteristic
150C43⋊C8—42no—
151#13073—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—22no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43#41611yescharacteristic
158C22×C43#46511yescharacteristic
159C22×C43#46611yescharacteristic
160C2×D43—82no—
161C2×D43—162no—
162C2×D43—161no—
163C2×D43—161no—
164C2×D43—162no—
165C4×C43—22no—
166C4×C43—161no—
167C4×C43#38611yescharacteristic
168C4×C43C2×#10211yescharacteristic
169C4×C43#46511yescharacteristic
170C4×C43#46611yescharacteristic
171C2×#504—431no—
172C2×#472—431no—
173C2×#361—431no—
174C2×#357—431no—
175#1816D4311yescharacteristic, complemented
176#1387—431no—
177#1381—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—42no—
181C2×C43#189311yescharacteristic
182C2×C43#222111yescharacteristic
183C2×C43#222311yescharacteristic
184D43—162no—
185C2×AGL(1,ℤ/8)—861no—
186C22×D8—431no—
187C2×#131C2×D4311yescharacteristic
188#504—862no—
189#504—862no—
190C2×M32—431no—
191C2×M32—861no—
192C22×C16—431no—
193C22×C16—861no—
194#472—434no—
195#472—862no—
196C2×#108—431no—
197C2×#108C2×D4311yescharacteristic
198C2×#107C2×D4311yescharacteristic
199#417—21no—
200C2×#100—861no—
201#361—862no—
202#357—861no—
203#357—861no—
204#343—21no—
205C43#1307311yescharacteristic, complemented, Sylow
206C2×#41C22⋊D4311yescharacteristic
207C22×D4—861no—
208AGL(1,ℤ/8)—864no—
209AGL(1,ℤ/8)—1722no—
210C2×SD16—1721no—
211C2×D8—432no—
212C2×D8—861no—
213C2×D8—861no—
214C2×D8—861no—
215C2×D8—861no—
216C2×D8—861no—
217C2×D8—1721no—
218#131—21no—
219#131—21no—
220#131C4×D4312yes—
221#131D17212yes—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—861no—
225C2×M16C22⋊D4311yescharacteristic
226C22×C8—21no—
227C22×C8C22×D4311yescharacteristic
228C2×C4⋊C4—21no—
229M32—432no—
230M32—864no—
231M32—861no—
232C2×C16—431no—
233C2×C16—431no—
234C2×C16—864no—
235C2×C16—861no—
236C2×C16—861no—
237C2×C16—861no—
238#108—21no—
239#108—21no—
240#108—432no—
241#108—861no—
242#107—21no—
243#107—21no—
244#103—41no—
245#102—41no—
246#100—864no—
247C24—1721no—
248#41—21no—
249#41—21no—
250#41(C2×D43)⋊C412yes—
251#41#1062188412yes—
252C2×Q8#1062188211yescharacteristic
253C2×D4—21no—
254C2×D4—862no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1721no—
258C2×D4—1721no—
259C2×D4—1721no—
260C2×D4#1062188211yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4C2×C22⋊D4311yescharacteristic
264SD16—1724no—
265D8—862no—
266D8—862no—
267D8—1724no—
268D8—1721no—
269D8—1721no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—41no—
274M16—41no—
275M16—862no—
276M16—1721no—
277M16(C2×D43)⋊C412yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—1721no—
283C2×C8C2×C4×D4311yescharacteristic
284C2×C8C2×D17211yescharacteristic
285C2×C8D4×D4311yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8#1062190011yescharacteristic
288C2×C8#1062190011yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—41no—
291C16—861no—
292C16—861no—
293C16—862no—
294C23—21no—
295C23—3441no—
296C23—3441no—
297C23—1722no—
298C23—6881no—
299C23—6881no—
300C23#1306334511yescharacteristic
301Q8—21no—
302Q8#1306324512yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—3441no—
307D4—3441no—
308D4—1722no—
309D4—1722no—
310D4#1306324512yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—81no—
315C2×C4—161no—
316C2×C4C2×(C2×D43)⋊C411yescharacteristic
317C2×C4#1306329711yescharacteristic
318C2×C4#1306329711yescharacteristic
319C2×C4C2×#1062188211yescharacteristic
320C2×C4C2×#1062188411yescharacteristic
321C2×C4#1306334511yescharacteristic
322C8—22no—
323C8—81no—
324C8—1722no—
325C8(C22⋊D43)⋊C411yescharacteristic
326C8(C22⋊D43)⋊C411yescharacteristic
327C8#1306329511yescharacteristic
328C8#1306330911yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—3442no—
335C22—6882no—
336C22—6882no—
337C22—6881no—
338C22—6881no—
339C22#1458289311yescharacteristic
340C22#1458313011yescharacteristic
341C22#1458313311yescharacteristic
342C4—22no—
343C4—161no—
344C4#1458277611yescharacteristic
345C4C2×#1306324511yescharacteristic
346C4#1458313011yescharacteristic
347C4#1458313311yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—6882no—
352C2#1913502111yescharacteristic
353C2#1913671311yescharacteristic
354C2#1913672711yescharacteristic
subgroupG/H
centerC22#14583133
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1816C2
socleC22×C43#466
prime radicalC2×#14583169C2
cosocleC22×C8×C43C23
hypercenter#1816D43
hypocenterC43#13073
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ #1816

Complements

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

NH ≅ G/Ntype
1. C2×#14583316C2semidirect
3. C2×#14582711C2semidirect
4. C2×#14582699C2semidirect
5. #19132703C2semidirect
6. #19132688C2semidirect
7. C43×#1816C2semidirect
17. #14583169C4semidirect
175. #1816D43semidirect
205. C43#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#145833162
C2×#145831692
C2×#145827112
C2×#145826992
#191327032
#191326882
C43×#18162
#1307343