Finite Group Databasebeta

← #25013684

Subgroups — #25013684

Order 11008.

462 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143512C211yesmaximal, characteristic, complemented
2#19136331C211yesmaximal, characteristic, complemented
3#19136323C211yesmaximal, characteristic, complemented
4#19135494C211yesmaximal, characteristic, complemented
5#19132691C211yesmaximal, characteristic, complemented
6#19132683C211yesmaximal, characteristic, complemented
7C2×C43×#508C211yesmaximal, characteristic
8#14583666—21no—
9C2×#13063265C2211yescharacteristic
10#14583021—22no—
11#14583016—22no—
12C2×#13063261C2211yescharacteristic
13#14582937C2211yescharacteristic
14#14582916—21no—
15#14582916—21no—
16#14582873—21no—
17#14582854C2211yescharacteristic
18#14582709—22no—
19#14582706—22no—
20C2×#135×C43C2211yescharacteristic
21C2×#135×C43C2211yescharacteristic
22C43×#508—22no—
23C43×#508—22no—
24C2×Q32×C43C411yescharacteristic, complemented
25C2×SD32×C43C411yescharacteristic, complemented
26C2×SD32×C43C411yescharacteristic, complemented
27C2×D16×C43C411yescharacteristic, complemented
28C22×C16×C43C2211yescharacteristic
29#13063332—24no—
30#13063332—42no—
31C2×#10621877—21no—
32C2×#10621877—42no—
33C2×#10621877D411yescharacteristic
34#13063284—21no—
35#13063284D411yescharacteristic
36#13063265—21no—
37#13063265—21no—
38C2×C43⋊C16—21no—
39#13063261—21no—
40#13063261D412yes—
41#13063259—21no—
42#13063257—21no—
43#13063252—24no—
44#13063252—42no—
45#13063240—42no—
46#13063235—21no—
47C8×Dic43—21no—
48C2×#41×C43—21no—
49C2×#41×C43—21no—
50#135×C43—21no—
51#135×C43—21no—
52#135×C43—21no—
53#135×C43—21no—
54#135×C43—21no—
55#135×C43—21no—
56#135×C43D412yes—
57#135×C43D412yes—
58C2×Q16×C43C2×C411yescharacteristic
59C2×Q16×C43C2×C411yescharacteristic
60C2×SD16×C43—21no—
61C2×SD16×C43—21no—
62C2×D8×C43C2×C411yescharacteristic
63C2×D8×C43C2×C411yescharacteristic
64C22×C8×C43C2311yescharacteristic
65Q32×C43—22no—
66SD32×C43—22no—
67SD32×C43—22no—
68D16×C43—22no—
69C2×C16×C43—21no—
70C2×C16×C43—21no—
71C2×C16×C43C2×C411yescharacteristic
72C2×C16×C43C2×C411yescharacteristic
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
90Q16×C43—21no—
91Q16×C43—21no—
92Q16×C43—21no—
93Q16×C43C22⋊C412yes—
94SD16×C43—22no—
95SD16×C43—22no—
96SD16×C43—41no—
97SD16×C43—41no—
98D8×C43—21no—
99D8×C43—21no—
100D8×C43—21no—
101D8×C43C22⋊C412yes—
102C2×C8×C43C22×C411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43#4111yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C22⋊Dic43—21no—
109C22⋊Dic43—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—41no—
112C4×Dic43—21no—
113C4×Dic43—41no—
114#10621877—21no—
115#10621877—22no—
116#10621877—44no—
117#10621877—41no—
118#10621877D812yes—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—44no—
121C2×C43⋊C8—41no—
122C16×C43—21no—
123C16×C43—21no—
124C43⋊C16—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43AGL(1,ℤ/8)11yescharacteristic
128Q8×C43—22no—
129Q8×C43—41no—
130Q8×C43—41no—
131Q8×C43—41no—
132D4×C43—22no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—41no—
136D4×C43—41no—
137D4×C43—41no—
138D4×C43—81no—
139D4×C43—81no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43C2×D811yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×Dic43—41no—
153C2×Dic43—81no—
154C8×C43C2×C22⋊C411yescharacteristic
155C8×C43C4×D411yescharacteristic
156C8×C43#12111yescharacteristic
157C8×C43#12311yescharacteristic
158C43⋊C8—22no—
159C43⋊C8—42no—
160#13016—431nomaximal, Sylow
161C22×C43—41no—
162C22×C43—42no—
163C22×C43—81no—
164C22×C43—161no—
165C22×C43—161no—
166C22×C43#44211yescharacteristic
167C22×C43#44911yescharacteristic
168C22×C43#45911yescharacteristic
169C4×C43—42no—
170C4×C43—81no—
171C4×C43#38611yescharacteristic
172C4×C43C4×D811yescharacteristic
173C4×C43#44711yescharacteristic
174C4×C43#46311yescharacteristic
175Dic43—81no—
176Dic43—161no—
177C2×#508D4311yescharacteristic
178#2957—431no—
179#2145—431no—
180#2143—431no—
181#1976—431no—
182#1382—431no—
183#1379—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—82no—
188C2×C43—161no—
189C2×C43#187911yescharacteristic
190C2×#135C2×D4311yescharacteristic
191C2×#135C2×D4311yescharacteristic
192#568—861no—
193#508—22no—
194#508—22no—
195C2×Q32Dic4311yescharacteristic, complemented
196C2×SD32Dic4311yescharacteristic, complemented
197C2×SD32Dic4311yescharacteristic, complemented
198C2×D16Dic4311yescharacteristic, complemented
199C2×M32—431no—
200C22×C16C2×D4311yescharacteristic
201#444—862no—
202#443—862no—
203C2×#108—431no—
204#427—431no—
205#421—861no—
206#421—861no—
207#410—861no—
208#405—431no—
209#360—862no—
210#359—862no—
211C43#1301611yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C2×#41—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135C22⋊D4312yes—
221#135C22⋊D4312yes—
222C2×Q16C2×Dic4311yescharacteristic
223C2×Q16C2×Dic4311yescharacteristic
224C2×SD16—21no—
225C2×SD16—21no—
226C2×D8C2×Dic4311yescharacteristic
227C2×D8C2×Dic4311yescharacteristic
228#131—864no—
229#131—1722no—
230C2×M16—431no—
231C2×M16—861no—
232C2×M16—1722no—
233C22×C8C22×D4311yescharacteristic
234#117—431no—
235#117—861no—
236Q32—22no—
237SD32—22no—
238SD32—22no—
239D16—22no—
240M32—861no—
241M32—861no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—861no—
245C2×C16C2×Dic4311yescharacteristic
246C2×C16C2×Dic4311yescharacteristic
247#108—432no—
248#108—861no—
249#107—861no—
250#106—861no—
251#104—864no—
252#104—1722no—
253#99—1722no—
254#97—861no—
255C4×C8—861no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—41no—
271C22×C4—41no—
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—432no—
286M16—861no—
287M16—862no—
288M16—1724no—
289M16—1721no—
290C2×C8—861no—
291C2×C8—1724no—
292C2×C8—1721no—
293C2×C8D4×D4311yescharacteristic
294C2×C8#1062190011yescharacteristic
295C2×C8#1062190011yescharacteristic
296C2×C8C22×Dic4311yescharacteristic
297C2×C8C2×C22⋊D4311yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C4⋊C4—861no—
300C4⋊C4—1721no—
301C22⋊C4—861no—
302C22⋊C4—1721no—
303C42—861no—
304C42—1721no—
305C16—21no—
306C16—21no—
307C16—1721no—
308C23—41no—
309C23—41no—
310C23#1306334911yescharacteristic
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—3441no—
330C2×C4—1721no—
331C2×C4D4×Dic4311yescharacteristic
332C2×C4#1306329311yescharacteristic
333C2×C4#1306329711yescharacteristic
334C2×C4D8×D4311yescharacteristic
335C2×C4#1306334411yescharacteristic
336C2×C4#1306334911yescharacteristic
337C8—862no—
338C8—1722no—
339C8C2×C22⋊Dic4311yescharacteristic
340C8D4×Dic4311yescharacteristic
341C8#1306329711yescharacteristic
342C8#1306330611yescharacteristic
343C22—41no—
344C22—42no—
345C22—81no—
346C22—161no—
347C22—161no—
348C22#1458301111yescharacteristic
349C22#1458304111yescharacteristic
350C22#1458309211yescharacteristic
351C4—42no—
352C4—81no—
353C4—3441no—
354C4—6881no—
355C4#1458277911yescharacteristic
356C4D8×Dic4311yescharacteristic
357C4#1458303111yescharacteristic
358C4#1458311211yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—161no—
364C2#1913494511yescharacteristic
subgroupG/H
centerC4#14583031
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC2×C43×#508C2
socleC2×C43#1879
cosocleC22×C8×C43C23
hypercenterC2×#508D43
hypocenterC43#13016
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. #19143512C2semidirect
2. #19136331C2semidirect
3. #19136323C2semidirect
4. #19135494C2semidirect
5. #19132691C2semidirect
6. #19132683C2semidirect
24. C2×Q32×C43C4semidirect
25. C2×SD32×C43C4semidirect
26. C2×SD32×C43C4semidirect
27. C2×D16×C43C4semidirect
195. C2×Q32Dic43semidirect
196. C2×SD32Dic43semidirect
197. C2×SD32Dic43semidirect
198. C2×D16Dic43semidirect
211. C43#13016semidirect

Maximal subgroups

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

subgroupindex
#191435122
#191363312
#191363232
#191354942
#191326912
#191326832
C2×C43×#5082
#1301643