Finite Group Databasebeta

← #25013740

Subgroups — #25013740

Order 11008.

466 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583021C211yesmaximal, characteristic, complemented
2#19136344C211yesmaximal, characteristic, complemented
3#19136323C211yesmaximal, characteristic, complemented
4#19135489C211yesmaximal, characteristic, complemented
5#19132707C211yesmaximal, characteristic, complemented
6#19132678C211yesmaximal, characteristic, complemented
7C43×#3414C211yesmaximal, characteristic
8C2×#13063332—21no—
9C2×#13063265C2211yescharacteristic
10#14583021—22no—
11#14583021—22no—
12C2×#13063261C2211yescharacteristic
13C2×#13063261C2211yescharacteristic
14C2×#13063252—21no—
15C2×#13063252—21no—
16#14582866—21no—
17C2×#13063235C2211yescharacteristic
18#14582715—21no—
19#14582712—21no—
20#14582706—22no—
21C2×#135×C43C2211yescharacteristic
22C2×#135×C43C2211yescharacteristic
23C43×#510—21no—
24C43×#510C412yescomplemented
25C43×#509—21no—
26C43×#509C412yescomplemented
27C43×#508—22no—
28C2×M32×C43C2211yescharacteristic
29#13063332—24no—
30#13063332—42no—
31C2×#10621877—21no—
32C2×#10621877—21no—
33C2×#10621877—41no—
34C22×C43⋊C8—41no—
35C22×C43⋊C8D411yescharacteristic
36C2×C4×Dic43D411yescharacteristic
37#13063265—21no—
38#13063265—21no—
39C2×C43⋊C16—21no—
40#13063261—21no—
41#13063261—21no—
42#13063261—21no—
43#13063261D412yes—
44#13063252—24no—
45#13063252—42no—
46C22⋊(C43⋊C8)—42no—
47#13063235—21no—
48#13063235—21no—
49C2×#41×C43—21no—
50C2×#41×C43—21no—
51#135×C43—21no—
52#135×C43—21no—
53#135×C43—21no—
54#135×C43—21no—
55#135×C43—21no—
56#135×C43—21no—
57#135×C43C2×C412yes—
58#135×C43D412yes—
59C2×Q16×C43C2×C411yescharacteristic
60C2×Q16×C43D411yescharacteristic
61C2×SD16×C43—21no—
62C2×SD16×C43—21no—
63C2×D8×C43C2×C411yescharacteristic
64C2×D8×C43D411yescharacteristic
65C22×C8×C43C2311yescharacteristic
66Q32×C43—22no—
67SD32×C43—22no—
68SD32×C43—22no—
69D16×C43—22no—
70M32×C43—21no—
71M32×C43C2×C412yes—
72C2×C16×C43—21no—
73#41×C43—22no—
74#41×C43—22no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80#41×C43—41no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—21no—
91Q16×C43—21no—
92Q16×C43—21no—
93Q16×C43—21no—
94Q16×C43C22⋊C412yes—
95SD16×C43—22no—
96SD16×C43—22no—
97SD16×C43—41no—
98SD16×C43—41no—
99D8×C43—21no—
100D8×C43—21no—
101D8×C43—21no—
102D8×C43C22⋊C412yes—
103C2×C8×C43C22×C411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C4×Dic43—21no—
110C4×Dic43—21no—
111#10621877—22no—
112#10621877—44no—
113#10621877—41no—
114#10621877—41no—
115#10621877—41no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—44no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8D812yes—
122C16×C43—22no—
123C43⋊C16—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43#13511yescharacteristic
127Q8×C43—22no—
128Q8×C43—41no—
129Q8×C43—41no—
130Q8×C43—41no—
131D4×C43—22no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—41no—
135D4×C43—41no—
136D4×C43—41no—
137D4×C43—81no—
138D4×C43—81no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—81no—
144C2×C4×C43—81no—
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43C2×D811yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×Dic43—41no—
152C2×Dic43—81no—
153C8×C43C2×C22⋊C411yescharacteristic
154C8×C43C4×D411yescharacteristic
155C8×C43#12111yescharacteristic
156C8×C43#12311yescharacteristic
157C43⋊C8—22no—
158C43⋊C8—42no—
159C43⋊C8—81no—
160#13024—431nomaximal, Sylow
161C22×C43—41no—
162C22×C43—42no—
163C22×C43—82no—
164C22×C43—82no—
165C22×C43—81no—
166C22×C43C4×D811yescharacteristic
167C22×C43#44911yescharacteristic
168C22×C43#46311yescharacteristic
169C4×C43—42no—
170C4×C43—81no—
171C4×C43#38611yescharacteristic
172C4×C43#44211yescharacteristic
173C4×C43#44711yescharacteristic
174C4×C43#45911yescharacteristic
175Dic43—81no—
176#3414D4311yescharacteristic
177C2×#444—431no—
178#2148—431no—
179#2143—431no—
180#1975—431no—
181#1388—431no—
182#1377—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—82no—
187C2×C43—161no—
188C2×C43#187911yescharacteristic
189C2×#135C2×D4311yescharacteristic
190C2×#135C2×D4311yescharacteristic
191C2×#131—861no—
192#510—21no—
193#510Dic4312yescomplemented
194#509—21no—
195#509Dic4312yescomplemented
196#508—22no—
197C2×M32—431no—
198C2×M32C2×D4311yescharacteristic
199#444—862no—
200#444—862no—
201C2×#108—431no—
202C2×#108—431no—
203C2×#104—861no—
204C2×#104—861no—
205#408—861no—
206C2×#97—431no—
207#362—861no—
208#361—861no—
209#359—862no—
210C43#1302411yescharacteristic, complemented, Sylow
211C2×#41—21no—
212C2×#41—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135C2×Dic4312yes—
220#135C22⋊D4312yes—
221C2×Q16C2×Dic4311yescharacteristic
222C2×Q16C22⋊D4311yescharacteristic
223C2×SD16—21no—
224C2×SD16—21no—
225C2×D8C2×Dic4311yescharacteristic
226C2×D8C22⋊D4311yescharacteristic
227#131—864no—
228#131—1722no—
229C2×M16—861no—
230C2×M16—861no—
231C2×M16—1721no—
232C22×C8—431no—
233C22×C8—1721no—
234C22×C8C22×D4311yescharacteristic
235C2×C42—431no—
236Q32—22no—
237SD32—22no—
238SD32—22no—
239D16—22no—
240M32—21no—
241M32—861no—
242M32—861no—
243M32C2×Dic4312yes—
244C2×C16—21no—
245C2×C16—861no—
246#108—432no—
247#108—861no—
248#108—861no—
249#108—861no—
250#104—864no—
251#104—1722no—
252C22⋊C8—1722no—
253#97—861no—
254#97—861no—
255#41—22no—
256#41—22no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—861no—
272C22×C4D4×D4311yescharacteristic
273Q16—21no—
274Q16—21no—
275Q16—21no—
276Q16C22⋊Dic4312yes—
277SD16—22no—
278SD16—22no—
279SD16—41no—
280SD16—41no—
281D8—21no—
282D8—21no—
283D8—21no—
284D8C22⋊Dic4312yes—
285M16—862no—
286M16—1724no—
287M16—1721no—
288M16—1721no—
289M16—1721no—
290C2×C8—432no—
291C2×C8—861no—
292C2×C8—861no—
293C2×C8—1724no—
294C2×C8—1721no—
295C2×C8—1721no—
296C2×C8D4×D4311yescharacteristic
297C2×C8#1062190011yescharacteristic
298C2×C8#1062190011yescharacteristic
299C2×C8C22×Dic4311yescharacteristic
300C2×C8C2×C22⋊D4311yescharacteristic
301C2×C8C2×C22⋊D4311yescharacteristic
302C42—861no—
303C42—861no—
304C16—22no—
305C16—1721no—
306C23—41no—
307C23—41no—
308C23#1306334411yescharacteristic
309Q8—22no—
310Q8—41no—
311Q8—41no—
312Q8—41no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—3441no—
328C2×C4—1721no—
329C2×C4D4×Dic4311yescharacteristic
330C2×C4#1306329311yescharacteristic
331C2×C4#1306329711yescharacteristic
332C2×C4D8×D4311yescharacteristic
333C2×C4#1306334911yescharacteristic
334C2×C4#1306334911yescharacteristic
335C8—862no—
336C8—3441no—
337C8—1722no—
338C8C2×C22⋊Dic4311yescharacteristic
339C8D4×Dic4311yescharacteristic
340C8#1306329711yescharacteristic
341C8#1306330611yescharacteristic
342C22—41no—
343C22—42no—
344C22—82no—
345C22—82no—
346C22—81no—
347C22D8×Dic4311yescharacteristic
348C22#1458304111yescharacteristic
349C22#1458311211yescharacteristic
350C4—42no—
351C4—81no—
352C4—3441no—
353C4#1458277911yescharacteristic
354C4#1458301111yescharacteristic
355C4#1458303111yescharacteristic
356C4#1458309211yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—82no—
361C2—161no—
362C2#1913494511yescharacteristic
subgroupG/H
centerC4#14583031
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC43×#3414C2
socleC2×C43#1879
cosocleC22×C8×C43C23
hypercenter#3414D43
hypocenterC43#13024
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. C2×#14583021C2semidirect
2. #19136344C2semidirect
3. #19136323C2semidirect
4. #19135489C2semidirect
5. #19132707C2semidirect
6. #19132678C2semidirect
24. C43×#510C4semidirect
26. C43×#509C4semidirect
193. #510Dic43semidirect
195. #509Dic43semidirect
210. C43#13024semidirect

Maximal subgroups

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

subgroupindex
C2×#145830212
#191363442
#191363232
#191354892
#191327072
#191326782
C43×#34142
#1302443