Finite Group Databasebeta

← #25014039

Subgroups — #25014039

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×#14583169C211yesmaximal, characteristic
2C2×#14582713C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic, complemented
4#19134659C211yesmaximal, characteristic, complemented
5#19132704C211yesmaximal, characteristic, complemented
6#19132689C211yesmaximal, characteristic, complemented
7C2×C43×#504C211yesmaximal, characteristic, complemented
8C2×#13063350—21no—
9C22×D344C2211yescharacteristic
10#14583169—22no—
11#14583169C414yescomplemented
12C2×#13063261C2211yescharacteristic
13C2×#13063261C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15#14582900—21no—
16C2×#13063241—21no—
17#14582713—22no—
18#14582701—21no—
19#14582701—21no—
20#14582667—21no—
21C2×#131×C43C2211yescharacteristic
22C43×#504—22no—
23C43×#504—22no—
24C2×M32×C43—21no—
25C2×M32×C43C2211yescharacteristic
26C22×C16×C43—21no—
27C22×C16×C43C2211yescharacteristic
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—
40C2×#10621877—21no—
41C2×C4⋊Dic43—21no—
42#13063261—21no—
43#13063261—21no—
44#13063261—21no—
45#13063261C2×C412yes—
46#13063259—21no—
47#13063259—21no—
48#13063249—41no—
49#13063246—41no—
50#13063241—24no—
51C2×#41×C43D411yescharacteristic
52#131×C43—21no—
53#131×C43—21no—
54#131×C43C2×C412yes—
55#131×C43D412yes—
56C2×M16×C43—21no—
57C2×M16×C43D411yescharacteristic
58C22×C8×C43—21no—
59C22×C8×C43C2311yescharacteristic
60M32×C43—24no—
61M32×C43—21no—
62M32×C43D412yes—
63C2×C16×C43—24no—
64C2×C16×C43—21no—
65C2×C16×C43—21no—
66C2×C16×C43—21no—
67C2×C16×C43D411yescharacteristic
68C2×C16×C43D411yescharacteristic
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×C43C2×D411yescharacteristic
79C22×Dic43—41no—
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×C43C22⋊C412yes—
90C2×C8×C43—21no—
91C2×C8×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43#4111yescharacteristic
98C2×C8×C43#4111yescharacteristic
99#10621884—44no—
100#10621882—44no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103#10621877—22no—
104#10621877—41no—
105#10621877—41no—
106#10621877—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109D344—22no—
110D344—22no—
111D344—41no—
112D344—41no—
113C16×C43—21no—
114C16×C43—22no—
115C16×C43—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×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43C2×D811yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×Dic43—81no—
139C2×Dic43—161no—
140D172—42no—
141D172—42no—
142D172—81no—
143D172—81no—
144C8×C43—22no—
145C8×C43C4×D411yescharacteristic
146C8×C43C4×D411yescharacteristic
147C8×C43#12011yescharacteristic
148C8×C43#12311yescharacteristic
149C43⋊C8—42no—
150C43⋊C8—81no—
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#38611yescharacteristic
167C4×C43C2×#10211yescharacteristic
168C4×C43#46511yescharacteristic
169C4×C43#46611yescharacteristic
170Dic43—161no—
171C2×#504D4311yescharacteristic, complemented
172C2×#472—431no—
173C2×#361—431no—
174C2×#357—431no—
175#1816—431no—
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—22no—
189#504—22no—
190C2×M32—21no—
191C2×M32C2×D4311yescharacteristic
192C22×C16—21no—
193C22×C16C2×D4311yescharacteristic
194#472—434no—
195#472—862no—
196C2×#108—431no—
197C2×#108—431no—
198C2×#107—431no—
199#417—861no—
200C2×#100—861no—
201#361—862no—
202#357—861no—
203#357—861no—
204#343—861no—
205C43#1307311yescharacteristic, complemented, Sylow
206C2×#41D17211yescharacteristic
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#131C22⋊D4312yes—
222C2×M16—21no—
223C2×M16—861no—
224C2×M16—861no—
225C2×M16D17211yescharacteristic
226C22×C8—21no—
227C22×C8C22×D4311yescharacteristic
228C2×C4⋊C4—861no—
229M32—24no—
230M32—21no—
231M32C22⋊D4312yes—
232C2×C16—24no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16C22⋊D4311yescharacteristic
237C2×C16C22⋊D4311yescharacteristic
238#108—432no—
239#108—861no—
240#108—861no—
241#108—861no—
242#107—861no—
243#107—861no—
244#103—1721no—
245#102—1721no—
246#100—864no—
247C24—1721no—
248#41—21no—
249#41—21no—
250#41#1062187312yes—
251#41(C2×D43)⋊C412yes—
252C2×Q8D34411yescharacteristic
253C2×D4—21no—
254C2×D4—862no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1721no—
258C2×D4—1721no—
259C2×D4—1721no—
260C2×D4D34411yescharacteristic
261C22×C4—21no—
262C22×C4—1721no—
263C22×C4C2×D17211yescharacteristic
264SD16—1724no—
265D8—862no—
266D8—862no—
267D8—1724no—
268D8—1721no—
269D8—1721no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—862no—
274M16—1721no—
275M16—1721no—
276M16—1721no—
277M16(C2×D43)⋊C412yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—1721no—
282C2×C8—1721no—
283C2×C8C2×C4×D4311yescharacteristic
284C2×C8#1062189811yescharacteristic
285C2×C8#1062189811yescharacteristic
286C2×C8C2×C22⋊D4311yescharacteristic
287C2×C8C2×C22⋊D4311yescharacteristic
288C2×C8C2×C22⋊D4311yescharacteristic
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C16—21no—
292C16—22no—
293C16—21no—
294C23—21no—
295C23—3441no—
296C23—3441no—
297C23—1722no—
298C23—6881no—
299C23—6881no—
300C23#1306334711yescharacteristic
301Q8—21no—
302Q8#1306324712yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—3441no—
307D4—3441no—
308D4—1722no—
309D4—1722no—
310D4#1306324712yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—3441no—
315C2×C4—6881no—
316C2×C4C2×(C2×D43)⋊C411yescharacteristic
317C2×C4#1306329911yescharacteristic
318C2×C4#1306329911yescharacteristic
319C2×C4C2×D34411yescharacteristic
320C2×C4C2×#1062187311yescharacteristic
321C2×C4#1306334711yescharacteristic
322C8—22no—
323C8—3441no—
324C8—1722no—
325C8C4×C22⋊D4311yescharacteristic
326C8C4×C22⋊D4311yescharacteristic
327C8#1306329411yescharacteristic
328C8#1306330811yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—3442no—
335C22—6882no—
336C22—6882no—
337C22—6881no—
338C22—6881no—
339C22#1458289611yescharacteristic
340C22#1458312811yescharacteristic
341C22#1458313511yescharacteristic
342C4—22no—
343C4—6881no—
344C4#1458277811yescharacteristic
345C4C2×#1306324711yescharacteristic
346C4#1458312811yescharacteristic
347C4#1458313511yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—6882no—
352C2#1913502311yescharacteristic
353C2#1913671511yescharacteristic
354C2#1913672511yescharacteristic
subgroupG/H
centerC22#14583135
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#504C2
socleC22×C43#466
prime radicalC2×#14583169C2
cosocleC22×C8×C43C23
hypercenterC2×#504D43
hypocenterC43#13073
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. C2×#14582713C2semidirect
3. C2×#14582701C2semidirect
4. #19134659C2semidirect
5. #19132704C2semidirect
6. #19132689C2semidirect
7. C2×C43×#504C2semidirect
11. #14583169C4semidirect
171. C2×#504D43semidirect
205. C43#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#145831692
C2×#145827132
C2×#145827012
#191346592
#191327042
#191326892
C2×C43×#5042
#1307343