Finite Group Databasebeta

← #25013557

Subgroups — #25013557

Order 11008.

476 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#19143206C211yesmaximal, characteristic, complemented
2#19136323C211yesmaximal, characteristic, complemented
3C2×#14582706C211yesmaximal, characteristic, complemented
4C2×#14582683C211yesmaximal, characteristic, complemented
5#19132708C211yesmaximal, characteristic, complemented
6#19132688C211yesmaximal, characteristic, complemented
7C43×#3067C211yesmaximal, characteristic
8#14583666—21no—
9C2×#13063265C2211yescharacteristic
10C22×C43⋊C16C2211yescharacteristic
11#14582948—22no—
12#14582948—21no—
13C2×#13063261—22no—
14C2×#13063261C2211yescharacteristic
15C2×#13063261C2211yescharacteristic
16#14582706—22no—
17#14582706—22no—
18#14582683—22no—
19C43×#575—21no—
20C2×#135×C43C2211yescharacteristic
21C2×#131×C43C2211yescharacteristic
22C43×#473C412yes—
23C43×#472C412yes—
24C43×#471—22no—
25C2×#108×C43C2211yescharacteristic
26C43×#413—21no—
27#13063332—42no—
28#13063332—42no—
29C2×#10621877—24no—
30C2×#10621877—21no—
31C2×#10621877—21no—
32#13063265—21no—
33#13063265—21no—
34C2×C43⋊C16—21no—
35C2×C43⋊C16—21no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38#13063261—24no—
39#13063261—21no—
40#13063261—21no—
41#13063261D412yes—
42#13063261D412yes—
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×C43D812yes—
78C2×Q8×C43—21no—
79C2×Q8×C43SD1611yescharacteristic
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—41no—
83C2×D4×C43SD1611yescharacteristic
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87Q16×C43—21no—
88Q16×C43—21no—
89Q16×C43—42no—
90SD16×C43—42no—
91SD16×C43—42no—
92SD16×C43—41no—
93SD16×C43—41no—
94D8×C43—21no—
95D8×C43—21no—
96D8×C43—42no—
97M16×C43—21no—
98M16×C43—22no—
99M16×C43—22no—
100M16×C43—22no—
101M16×C43—41no—
102M16×C43C22⋊C412yes—
103C2×C8×C43—21no—
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43—41no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C2×C8×C43#4111yescharacteristic
113#10621877—22no—
114#10621877—22no—
115#10621877—44no—
116#10621877—41no—
117#10621877—41no—
118C2×C43⋊C8—44no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C43⋊C16—41no—
122C43⋊C16—41no—
123C23×C43—21no—
124C23×C43—41no—
125C23×C43#13711yescharacteristic
126Q8×C43—21no—
127Q8×C43—41no—
128Q8×C43—41no—
129Q8×C43#10212yes—
130D4×C43—22no—
131D4×C43—22no—
132D4×C43—21no—
133D4×C43—41no—
134D4×C43—41no—
135D4×C43—81no—
136D4×C43—81no—
137D4×C43#10212yes—
138C2×C4×C43—21no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12311yescharacteristic
147C2×C4×C43C2×D811yescharacteristic
148C2×C4×C43C2×SD1611yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150C8×C43—22no—
151C8×C43—42no—
152C8×C43C4×D411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12111yescharacteristic
156C43⋊C8—42no—
157C43⋊C8—42no—
158#12995—431nomaximal, Sylow
159C22×C43—22no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43—161no—
164C22×C43#41711yescharacteristic
165C22×C43#44811yescharacteristic
166C22×C43#48011yescharacteristic
167C4×C43—22no—
168C4×C43—81no—
169C4×C43#38611yescharacteristic
170C4×C43C2×#10211yescharacteristic
171C4×C43#44711yescharacteristic
172C4×C43#48111yescharacteristic
173#3067D4311yescharacteristic
174#2916—431no—
175#2143—431no—
176C2×#359—431no—
177C2×#350—431no—
178#1388—431no—
179#1381—431no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—42no—
184C2×C43—161no—
185C2×C43#187411yescharacteristic
186#575—21no—
187C2×#135C2×D4311yescharacteristic
188#568—861no—
189C2×#131C2×D4311yescharacteristic
190C2×M32—431no—
191C22×C16—431no—
192#473Dic4312yes—
193#472Dic4312yes—
194#471—22no—
195#430—862no—
196#430—861no—
197C2×#108—431no—
198C2×#108—431no—
199C2×#108—862no—
200C2×#108C2×D4311yescharacteristic
201#413—21no—
202#359—862no—
203#359—862no—
204#350—862no—
205C43#1299511yescharacteristic, 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#131—1722no—
223#131—1722no—
224#131C2×Dic4312yes—
225#131C22⋊D4312yes—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—864no—
229C2×M16—861no—
230C2×M16—861no—
231C2×M16C22⋊D4311yescharacteristic
232C22×C8—21no—
233C22×C8C22×D4311yescharacteristic
234M32—861no—
235M32—861no—
236C2×C16—861no—
237C2×C16—861no—
238C2×C16—861no—
239C2×C16—861no—
240#108—21no—
241#108—432no—
242#108—432no—
243#108—864no—
244#108—861no—
245#108—861no—
246#108C2×Dic4312yes—
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#1062188212yes—
256#41C22⋊Dic4312yes—
257C2×Q8—21no—
258C2×Q8#1062188311yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4#1062188311yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4C2×C22⋊D4311yescharacteristic
266Q16—21no—
267Q16—21no—
268Q16—42no—
269SD16—42no—
270SD16—42no—
271SD16—41no—
272SD16—41no—
273D8—21no—
274D8—21no—
275D8—42no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—41no—
281M16—862no—
282M16—862no—
283M16—1724no—
284M16—1721no—
285M16—1721no—
286M16C22⋊Dic4312yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—1724no—
292C2×C8—1721no—
293C2×C8—1721no—
294C2×C8D4×D4311yescharacteristic
295C2×C8D4×D4311yescharacteristic
296C2×C8#1062190011yescharacteristic
297C2×C8#1062190011yescharacteristic
298C2×C8C22×Dic4311yescharacteristic
299C2×C8C2×C22⋊D4311yescharacteristic
300C16—1721no—
301C16—1721no—
302C23—21no—
303C23—41no—
304C23#1306335511yescharacteristic
305Q8—21no—
306Q8—41no—
307Q8—41no—
308Q8#1306324612yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316D4#1306324612yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊Dic4311yescharacteristic
324C2×C4#1306329311yescharacteristic
325C2×C4#1306330611yescharacteristic
326C2×C4C2×#1062188211yescharacteristic
327C2×C4C2×#1062188311yescharacteristic
328C2×C4#1306335011yescharacteristic
329C8—22no—
330C8—42no—
331C8—1722no—
332C8—1722no—
333C8D4×Dic4311yescharacteristic
334C8D4×Dic4311yescharacteristic
335C8#1306329711yescharacteristic
336C8#1306329711yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—81no—
341C22—161no—
342C22#1458290011yescharacteristic
343C22#1458303711yescharacteristic
344C22#1458321011yescharacteristic
345C4—22no—
346C4—81no—
347C4#1458277911yescharacteristic
348C4C2×#1306324611yescharacteristic
349C4#1458303211yescharacteristic
350C4#1458321511yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2#1913491311yescharacteristic
subgroupG/H
centerC4#14583032
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC43×#3067C2
socleC2×C43#1874
cosocleC22×C8×C43C23
hypercenter#3067D43
hypocenterC43#12995
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. #19143206C2semidirect
2. #19136323C2semidirect
3. C2×#14582706C2semidirect
4. C2×#14582683C2semidirect
5. #19132708C2semidirect
6. #19132688C2semidirect
205. C43#12995semidirect

Maximal subgroups

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

subgroupindex
#191432062
#191363232
C2×#145827062
C2×#145826832
#191327082
#191326882
C43×#30672
#1299543