Finite Group Databasebeta

← #24988013

Subgroups — #24988013

Order 11008.

710 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148028C211yesmaximal, characteristic
2#19135532C211yesmaximal, characteristic, complemented
3#19132983C212yesmaximal, complemented
4#19132975C212yesmaximal, complemented
5C43×#1461C211yesmaximal, characteristic, complemented
6#14583530C411yescharacteristic
7#14583521—22no—
8#14583507—22no—
9#14583496—22no—
10#14583480C411yescharacteristic
11#14583473C412yes—
12#14583453—22no—
13#14583436—22no—
14#14583433—22no—
15C4×#10621898C2212yes—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×C4×C43⋊C8C2211yescharacteristic
18#14582654—22no—
19#14582631—22no—
20#14582629—22no—
21#14582628—22no—
22#14582626—22no—
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#431C2212yes—
25C43×#324—22no—
26C2×#10621898C2×C412yes—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29#13063324—22no—
30#13063323—22no—
31#13063320—24no—
32#13063319—24no—
33#13063317—22no—
34#13063316—22no—
35#13063315—24no—
36#13063314—22no—
37#13063313—22no—
38#13063310—24no—
39#13063308—24no—
40#13063305—22no—
41#13063304—22no—
42#13063303—24no—
43#13063301—22no—
44#13063301—22no—
45#13063300—22no—
46#13063299—22no—
47C4×Dic86—22no—
48C4×Dic86D412yes—
49C4×Dic86D412yes—
50C4×D172—22no—
51C4×D172D412yes—
52C4×D172D412yes—
53C4×C22⋊D43—22no—
54C4×C22⋊D43—22no—
55#13063284C2×C412yes—
56#13063282—24no—
57#13063282—22no—
58C42×D43—22no—
59C4⋊(C43⋊C8)—22no—
60C4×C43⋊C8—22no—
61C22×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43—22no—
63C4×Q8×C43—22no—
64C2×C4⋊C4×C43C2×C411yescharacteristic
65C2×C4⋊C4×C43D412yes—
66C2×C42×C43D412yes—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—22no—
69C22⋊C8×C43—22no—
70C4×C8×C43—22no—
71C2×Q8×C43—22no—
72C2×Q8×C43—22no—
73C2×Q8×C43—22no—
74C22×C4×C43C22⋊C412yes—
75C22×C4×C43C22⋊C412yes—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C2×C22⋊D43—22no—
80#10621898—24no—
81#10621898—24no—
82C2×D172—22no—
83C2×D172C22⋊C412yes—
84C2×C4×D43—22no—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×Dic86—22no—
88C2×Dic86C22⋊C412yes—
89C2×C8×C43—42no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—24no—
92C42×C43—22no—
93C42×C43—22no—
94C42×C43C2×D412yes—
95C42×C43C2×D412yes—
96C22⋊Dic43—22no—
97(C2×D43)⋊C4—24no—
98(C2×D43)⋊C4—24no—
99(C2×D43)⋊C4—24no—
100(C2×D43)⋊C4—22no—
101(C2×D43)⋊C4—22no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4⋊Dic43C22⋊C412yes—
105C4⋊Dic43C22⋊C412yes—
106Dic43⋊C4—24no—
107Dic43⋊C4—24no—
108Dic43⋊C4—24no—
109Dic43⋊C4—22no—
110Dic43⋊C4—22no—
111C4×Dic43—22no—
112C4×Dic43—22no—
113C4×Dic43—22no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—42no—
118C2×C43⋊C8—41no—
119C23×C43C2×C22⋊C411yescharacteristic
120C22×D43—22no—
121Q8×C43—44no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43C2×C22⋊C412yes—
131C2×C4×C43#12012yes—
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#13112yes—
135C2×C4×C43#13112yes—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C2×Dic43—22no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141D172—24no—
142D172—82no—
143C4×D43—44no—
144C4×D43—42no—
145C4×D43—42no—
146C4×D43—82no—
147Dic86—24no—
148Dic86—82no—
149C8×C43—82no—
150C43⋊C8—42no—
151C43⋊C8—81no—
152#8321—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43#37911yescharacteristic
156C22×C43#40811yescharacteristic
157C22×C43#40811yescharacteristic
158C2×D43—42no—
159C2×D43—42no—
160C2×D43—42no—
161C4×C43—21no—
162C4×C43—22no—
163C4×C43—42no—
164C4×C43—42no—
165C4×C43#40814yes—
166C4×C43#45411yescharacteristic
167C4×C43#45611yescharacteristic
168Dic43—42no—
169Dic43—42no—
170Dic43—42no—
171#3461—431no—
172#1984—431no—
173#1477—432no—
174#1476—432no—
175#1461D4311yescharacteristic, complemented
176C2×C43—21no—
177C2×C43—21no—
178C2×C43#178011yescharacteristic
179C2×C43#179311yescharacteristic
180C2×C43#179411yescharacteristic
181D43—82no—
182#544—431no—
183#542—862no—
184#541—862no—
185#539—862no—
186#537—431no—
187#536—432no—
188#533—862no—
189#529—862no—
190#529—862no—
191C4×#41—432no—
192C2×C4×Q8C2×D4311yescharacteristic
193#431C2×D4312yes—
194C2×C4⋊C8—431no—
195C2×C4×C8—431no—
196#336—862no—
197Q8⋊C8—862no—
198Q8⋊C8—862no—
199D4⋊C8—862no—
200D4⋊C8—862no—
201#324—22no—
202C43#832111yescharacteristic, complemented, Sylow
203C2×#41—432no—
204C22×Q8C4×D4311yescharacteristic
205C22×C8—861no—
206C22×C8—861no—
207C4⋊Q8—862no—
208C4⋊Q8—862no—
209#126—864no—
210#126—864no—
211#125—862no—
212#125—862no—
213#125—864no—
214#124—862no—
215#124—862no—
216#123—864no—
217#123—864no—
218C22⋊Q8—862no—
219C22⋊Q8—864no—
220C22⋊Q8—862no—
221C22⋊Q8—862no—
222C22⋊Q8—862no—
223#121—862no—
224#121—862no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—432no—
228C4×Q8—432no—
229C4×Q8—862no—
230C4×D4—432no—
231C4×D4—432no—
232C4×D4—862no—
233C4×D4—862no—
234C4×D4—862no—
235#117—432no—
236#117—864no—
237#117—862no—
238C2×C4⋊C4C4×D4311yescharacteristic
239C2×C4⋊C4C22⋊D4312yes—
240C2×C42—862no—
241C2×C42D17212yes—
242C2×C42C22×D4311yescharacteristic
243C4⋊C8—22no—
244C4⋊C8—862no—
245C22⋊C8—22no—
246C4×C8—22no—
247C4×C8—862no—
248#41—864no—
249#41—864no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—432no—
254C2×Q8—862no—
255C2×D4—432no—
256C2×D4—862no—
257C2×D4—862no—
258C22×C4—862no—
259C22×C4—862no—
260C22×C4—862no—
261C22×C4(C2×D43)⋊C412yes—
262C22×C4(C2×D43)⋊C412yes—
263C22×C4C2×C4×D4311yescharacteristic
264C22×C4C2×D17211yescharacteristic
265C22×C4C2×C22⋊D4311yescharacteristic
266C2×C8—42no—
267C2×C8—862no—
268C2×C8—1722no—
269C2×C8—1721no—
270C2×C8—1721no—
271C2×C8—1721no—
272C4⋊C4—22no—
273C4⋊C4—24no—
274C4⋊C4—432no—
275C4⋊C4—432no—
276C4⋊C4—864no—
277C4⋊C4—864no—
278C4⋊C4—862no—
279C4⋊C4—862no—
280C4⋊C4—864no—
281C4⋊C4—862no—
282C4⋊C4—862no—
283C22⋊C4—864no—
284C22⋊C4—864no—
285C22⋊C4—864no—
286C22⋊C4—862no—
287C22⋊C4—862no—
288C22⋊C4—862no—
289C42—22no—
290C42—22no—
291C42—862no—
292C42—862no—
293C42—862no—
294C42D4×D4312yes—
295C42D4×D4312yes—
296C23—862no—
297C23C2×(C2×D43)⋊C411yescharacteristic
298Q8—44no—
299Q8—864no—
300Q8—3442no—
301D4—864no—
302D4—3442no—
303D4—1722no—
304D4—1722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—862no—
314C2×C4—862no—
315C2×C4—862no—
316C2×C4—3442no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4—1724no—
320C2×C4C22⋊C4×D4312yes—
321C2×C4#1306329312yes—
322C2×C4#1306329511yescharacteristic
323C2×C4#1306329511yescharacteristic
324C2×C4#1306333112yes—
325C2×C4#1306333312yes—
326C8—82no—
327C8—3441no—
328C8—1722no—
329C22—21no—
330C22—21no—
331C22—1722no—
332C22—1722no—
333C22—1722no—
334C22#1458275411yescharacteristic
335C22#1458286511yescharacteristic
336C22#1458286711yescharacteristic
337C4—21no—
338C4—22no—
339C4—42no—
340C4—42no—
341C4—1722no—
342C4—1722no—
343C4—1722no—
344C4#1458286414yes—
345C4#1458307411yescharacteristic
346C4#1458308411yescharacteristic
347C2—21no—
348C2—21no—
349C2—3442no—
350C2#1913450611yescharacteristic
351C2#1913455611yescharacteristic
352C2#1913456111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1461C2
socleC22×C43#379
prime radical#14583480C4
cosocleC2×C42×C43C23
hypercenter#1461D43
hypocenterC43#8321
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #19135532C2semidirect
3. #19132983C2semidirect
4. #19132975C2semidirect
5. C43×#1461C2semidirect
175. #1461D43semidirect
202. C43#8321semidirect

Maximal subgroups

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

subgroupindex
#191480282
#191355322
#191329832
#191329752
C43×#14612
#832143