Finite Group Databasebeta

← #25014020

Subgroups — #25014020

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147698C211yesmaximal, characteristic, complemented
2C2×#14582709C211yesmaximal, characteristic, complemented
3#19136323C211yesmaximal, characteristic, complemented
4#19134654C211yesmaximal, characteristic, complemented
5#19132706C211yesmaximal, characteristic, complemented
6#19132695C211yesmaximal, characteristic, complemented
7C43×#3067C211yesmaximal, characteristic
8#14583316—22no—
9#14583316—22no—
10C2×#13063265—22no—
11C2×#13063265C2211yescharacteristic
12C2×#13063265C2211yescharacteristic
13C2×#13063261C2211yescharacteristic
14C2×#13063257C2211yescharacteristic
15#14582900—21no—
16#14582709—22no—
17#14582706—22no—
18#14582667—21no—
19C43×#575—21no—
20C2×#135×C43C2211yescharacteristic
21C2×#131×C43C2211yescharacteristic
22C43×#473C412yescomplemented
23C43×#472C412yescomplemented
24C43×#471—22no—
25C2×#108×C43C2211yescharacteristic
26C43×#413—21no—
27C2×#10621877—21no—
28C2×C4⋊Dic43—21no—
29#13063265—24no—
30#13063265—21no—
31#13063265—21no—
32#13063265—21no—
33#13063265D412yes—
34C2×C43⋊C16—24no—
35C2×C43⋊C16—21no—
36C2×C43⋊C16D412yes—
37#13063261—21no—
38#13063261—21no—
39#13063257—21no—
40#13063257—21no—
41#13063249—41no—
42#13063246—41no—
43C2×#41×C43—21no—
44C2×#41×C43D411yescharacteristic
45#137×C43—22no—
46#137×C43—41no—
47AGL(1,ℤ/8)×C43—22no—
48AGL(1,ℤ/8)×C43—41no—
49#135×C43—21no—
50#135×C43—21no—
51#135×C43—21no—
52#135×C43—21no—
53#135×C43—42no—
54C2×Q16×C43C2×C411yescharacteristic
55C2×SD16×C43—21no—
56C2×D8×C43C2×C411yescharacteristic
57#131×C43—21no—
58#131×C43—21no—
59#131×C43C2×C412yes—
60#131×C43D412yes—
61C2×M16×C43—21no—
62C2×M16×C43—21no—
63C2×M16×C43D411yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43C2311yescharacteristic
66#108×C43—21no—
67#108×C43C2×C412yes—
68#101×C43—22no—
69#100×C43—22no—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43—41no—
73#41×C43—41no—
74#41×C43—41no—
75#41×C43—41no—
76#41×C43C22⋊C412yes—
77#41×C43SD1612yes—
78C2×Q8×C43—21no—
79C2×Q8×C43D811yescharacteristic
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—41no—
83C2×D4×C43D811yescharacteristic
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C22×Dic43—41no—
88Q16×C43—21no—
89Q16×C43—21no—
90Q16×C43—42no—
91SD16×C43—42no—
92SD16×C43—42no—
93SD16×C43—41no—
94SD16×C43—41no—
95D8×C43—21no—
96D8×C43—21no—
97D8×C43—42no—
98M16×C43—21no—
99M16×C43—22no—
100M16×C43—22no—
101M16×C43—22no—
102M16×C43—41no—
103M16×C43C22⋊C412yes—
104C2×C8×C43—21no—
105C2×C8×C43—22no—
106C2×C8×C43—22no—
107C2×C8×C43—41no—
108C2×C8×C43C22×C411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43#4111yescharacteristic
113C2×C8×C43#4111yescharacteristic
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116#10621877—41no—
117#10621877—41no—
118C2×C43⋊C8—41no—
119C43⋊C16—22no—
120C43⋊C16—22no—
121C23×C43—21no—
122C23×C43—41no—
123C23×C43#13511yescharacteristic
124Q8×C43—21no—
125Q8×C43—41no—
126Q8×C43—41no—
127Q8×C43#10212yes—
128D4×C43—22no—
129D4×C43—22no—
130D4×C43—21no—
131D4×C43—41no—
132D4×C43—41no—
133D4×C43—81no—
134D4×C43—81no—
135D4×C43#10212yes—
136C2×C4×C43—21no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43C2×D811yescharacteristic
146C2×C4×C43C2×SD1611yescharacteristic
147C2×C4×C43#13511yescharacteristic
148C2×Dic43—81no—
149C2×Dic43—161no—
150C8×C43—22no—
151C8×C43—42no—
152C8×C43C4×D411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12011yescharacteristic
155C8×C43#12311yescharacteristic
156C43⋊C8—81no—
157#13070—431nomaximal, Sylow
158C22×C43—22no—
159C22×C43—41no—
160C22×C43—81no—
161C22×C43—81no—
162C22×C43—161no—
163C22×C43#41611yescharacteristic
164C22×C43#46511yescharacteristic
165C22×C43#46611yescharacteristic
166C4×C43—22no—
167C4×C43—81no—
168C4×C43#38611yescharacteristic
169C4×C43C2×#10211yescharacteristic
170C4×C43#46511yescharacteristic
171C4×C43#46611yescharacteristic
172Dic43—161no—
173#3407—431no—
174#3067D4311yescharacteristic
175C2×#360—431no—
176#2143—431no—
177#1815—431no—
178#1388—431no—
179#1383—431no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—42no—
184C2×C43—161no—
185C2×C43#189311yescharacteristic
186#575—21no—
187C2×#135C2×D4311yescharacteristic
188C2×#131C2×D4311yescharacteristic
189#504—862no—
190#504—862no—
191C2×M32—431no—
192C2×M32—431no—
193C2×M32—862no—
194#473Dic4312yescomplemented
195#472Dic4312yescomplemented
196#471—22no—
197C2×#108—431no—
198C2×#108C2×D4311yescharacteristic
199C2×#106—431no—
200#417—861no—
201#413—21no—
202#360—862no—
203#359—862no—
204#343—861no—
205C43#1307011yescharacteristic, complemented, Sylow
206C2×#41—21no—
207C2×#41C22⋊D4311yescharacteristic
208#137—22no—
209#137—41no—
210AGL(1,ℤ/8)—22no—
211AGL(1,ℤ/8)—41no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—42no—
217C2×Q16C2×Dic4311yescharacteristic
218C2×SD16—21no—
219C2×D8C2×Dic4311yescharacteristic
220#131—21no—
221#131—21no—
222#131C2×Dic4312yes—
223#131C22⋊D4312yes—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—861no—
227C2×M16C22⋊D4311yescharacteristic
228C22×C8—21no—
229C22×C8C22×D4311yescharacteristic
230C2×C4⋊C4—861no—
231M32—432no—
232M32—864no—
233M32—861no—
234M32—861no—
235M32—861no—
236C2×C16—432no—
237C2×C16—864no—
238C2×C16—861no—
239#108—21no—
240#108—861no—
241#108—861no—
242#108C2×Dic4312yes—
243#106—861no—
244#106—861no—
245#103—1721no—
246#102—1721no—
247#101—22no—
248#100—22no—
249#41—21no—
250#41—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255#41#1062188312yes—
256#41C22⋊Dic4312yes—
257C2×Q8—21no—
258C2×Q8#1062188211yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4#1062188211yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—1721no—
266C22×C4C2×C22⋊D4311yescharacteristic
267Q16—21no—
268Q16—21no—
269Q16—42no—
270SD16—42no—
271SD16—42no—
272SD16—41no—
273SD16—41no—
274D8—21no—
275D8—21no—
276D8—42no—
277M16—21no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—41no—
282M16—1721no—
283M16—1721no—
284M16C22⋊Dic4312yes—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—1721no—
290C2×C8D4×D4311yescharacteristic
291C2×C8D4×D4311yescharacteristic
292C2×C8#1062190011yescharacteristic
293C2×C8#1062190011yescharacteristic
294C2×C8C22×Dic4311yescharacteristic
295C2×C8C2×C22⋊D4311yescharacteristic
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C16—862no—
299C16—862no—
300C23—21no—
301C23—41no—
302C23#1306334511yescharacteristic
303Q8—21no—
304Q8—41no—
305Q8—41no—
306Q8#1306324612yes—
307D4—22no—
308D4—22no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—81no—
313D4—81no—
314D4#1306324612yes—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—3441no—
322C2×C4—6881no—
323C2×C4C2×C22⋊Dic4311yescharacteristic
324C2×C4#1306329711yescharacteristic
325C2×C4#1306329711yescharacteristic
326C2×C4C2×#1062188211yescharacteristic
327C2×C4C2×#1062188311yescharacteristic
328C2×C4#1306334511yescharacteristic
329C8—22no—
330C8—42no—
331C8—3441no—
332C8D4×Dic4311yescharacteristic
333C8D4×Dic4311yescharacteristic
334C8#1306329311yescharacteristic
335C8#1306330611yescharacteristic
336C22—22no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22—161no—
341C22#1458289511yescharacteristic
342C22#1458312611yescharacteristic
343C22#1458313311yescharacteristic
344C4—22no—
345C4—81no—
346C4—6881no—
347C4#1458277911yescharacteristic
348C4C2×#1306324611yescharacteristic
349C4#1458312611yescharacteristic
350C4#1458313311yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2#1913502411yescharacteristic
subgroupG/H
centerC2#19135024
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC43×#3067C2
socleC2×C43#1893
cosocleC22×C8×C43C23
hypercenter#3067D43
hypocenterC43#13070
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. #19147698C2semidirect
2. C2×#14582709C2semidirect
3. #19136323C2semidirect
4. #19134654C2semidirect
5. #19132706C2semidirect
6. #19132695C2semidirect
22. C43×#473C4semidirect
23. C43×#472C4semidirect
194. #473Dic43semidirect
195. #472Dic43semidirect
205. C43#13070semidirect

Maximal subgroups

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

subgroupindex
#191476982
C2×#145827092
#191363232
#191346542
#191327062
#191326952
C43×#30672
#1307043