Finite Group Databasebeta

← #24988437

Subgroups — #24988437

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic
2#19134579C211yesmaximal, characteristic
3#19133250C212yesmaximal, complemented
4#19132999C212yesmaximal, complemented
5C43×#1458C211yesmaximal, characteristic
6#14583530—21no—
7#14583530C412yes—
8#14583527—22no—
9#14583527—22no—
10#14583525—21no—
11#14583525C412yes—
12#14583456—21no—
13#14583456C2212yes—
14#14583452—24no—
15C2×#13063284—21no—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×C4⋊(C43⋊C8)C2211yescharacteristic
18C2×C22⋊(C43⋊C8)—21no—
19#14582654—21no—
20#14582647—22no—
21#14582646—22no—
22#14582631—24no—
23C2×#117×C43C2211yescharacteristic
24C43×#431C2212yes—
25C43×#324—21no—
26C43×#323—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29#13063325—21no—
30#13063325—21no—
31#13063325D412yes—
32#13063325D412yes—
33#13063324—24no—
34#13063324—24no—
35#13063317—22no—
36#13063317—22no—
37#13063316—24no—
38#13063316—24no—
39#13063304—22no—
40#13063304—22no—
41#13063304—22no—
42#13063304C2×C414yes—
43#13063302—24no—
44#13063302—24no—
45#13063302—24no—
46#13063302—24no—
47C4×Dic86—22no—
48C4×Dic86—22no—
49C4×Dic86—22no—
50C4×Dic86D414yes—
51#13063284—22no—
52#13063284—22no—
53#13063284—22no—
54#13063284—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C22⋊Dic43—22no—
58C2×C4×Dic43—22no—
59C4⋊(C43⋊C8)—22no—
60C4⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)—42no—
62C23×C4×C43D411yescharacteristic
63#117×C43—22no—
64#117×C43—22no—
65C2×C4⋊C4×C43C2×C411yescharacteristic
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C22⋊C4×C43C2×C411yescharacteristic
68C2×C22⋊C4×C43D411yescharacteristic
69C2×C42×C43D411yescharacteristic
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—22no—
72C22⋊C8×C43—22no—
73C4×C8×C43—22no—
74C24×C43C22⋊C411yescharacteristic
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43SD1612yes—
83C22×C4×C43Q1612yes—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×Dic43—22no—
88C22×Dic43—22no—
89C2×Dic86—22no—
90C2×Dic86—22no—
91C2×Dic86—22no—
92C2×Dic86C22⋊C414yes—
93C2×C8×C43—42no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—22no—
96C22⋊C4×C43—22no—
97C22⋊C4×C43—22no—
98C42×C43—21no—
99C42×C43—21no—
100C42×C43C2×D412yes—
101C42×C43C2×D412yes—
102C22⋊Dic43—24no—
103C22⋊Dic43—24no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43—22no—
107C4⋊Dic43—22no—
108C4⋊Dic43—22no—
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43C22⋊C414yes—
112Dic43⋊C4—24no—
113Dic43⋊C4—24no—
114Dic43⋊C4—24no—
115Dic43⋊C4—24no—
116C4×Dic43—24no—
117C4×Dic43—24no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43#10312yes—
129C23×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43#10312yes—
143C2×C4×C43C2×C22⋊C412yes—
144C2×C4×C43#12012yes—
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43C2×SD1611yescharacteristic
148C2×C4×C43C2×Q1611yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C2×C4×C43#13711yescharacteristic
151C2×Dic43—24no—
152C2×Dic43—24no—
153C2×Dic43—82no—
154C2×Dic43—82no—
155Dic86—44no—
156Dic86—82no—
157Dic86—82no—
158Dic86—82no—
159C8×C43—82no—
160C43⋊C8—81no—
161C43⋊C8—81no—
162#8410—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—22no—
166C22×C43—42no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—81no—
170C22×C43#37911yescharacteristic
171C22×C43C2×#10311yescharacteristic
172C22×C43#41911yescharacteristic
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43#44811yescharacteristic
179C4×C43#44811yescharacteristic
180C4×C43#45111yescharacteristic
181C4×C43#45111yescharacteristic
182Dic43—44no—
183Dic43—44no—
184#3458—431no—
185#1798—431no—
186#1542—432no—
187#1481—432no—
188#1458D4311yescharacteristic
189C2×C43—21no—
190C2×C43—21no—
191C2×C43—42no—
192C2×C43#178711yescharacteristic
193C2×C43#179111yescharacteristic
194C2×C43#179411yescharacteristic
195#544—432no—
196#544—862no—
197#544—862no—
198#544—861no—
199#543—432no—
200#543—861no—
201#533—432no—
202#533—864no—
203#533—861no—
204C2×#117—861no—
205C2×#117C2×D4311yescharacteristic
206#431C2×D4312yes—
207C2×C4⋊C8—431no—
208C2×C4⋊C8—431no—
209C2×C22⋊C8—861no—
210#336—861no—
211#333—862no—
212#332—862no—
213Q8⋊C8—864no—
214#324—21no—
215#323—21no—
216C43#841011yescharacteristic, complemented, Sylow
217C23×C4D17211yescharacteristic
218C22×C8—861no—
219C22×C8—861no—
220C4⋊Q8—432no—
221C4⋊Q8—432no—
222C4⋊Q8—861no—
223C4⋊Q8—861no—
224C4⋊Q8—864no—
225C4⋊Q8—864no—
226#125—862no—
227#125—864no—
228#125—864no—
229#125—862no—
230C22⋊Q8—434no—
231C22⋊Q8—864no—
232C22⋊Q8—864no—
233C22⋊Q8—864no—
234C22⋊Q8—864no—
235C22⋊Q8—862no—
236C22⋊Q8—862no—
237C22⋊Q8—862no—
238C4×Q8—434no—
239C4×Q8—862no—
240C4×Q8—862no—
241C4×Q8—862no—
242#117—22no—
243#117—22no—
244#117—862no—
245#117—862no—
246#117—862no—
247#117—862no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4C4×D4311yescharacteristic
251C2×C4⋊C4C22⋊D4311yescharacteristic
252C2×C22⋊C4—862no—
253C2×C22⋊C4C4×D4311yescharacteristic
254C2×C22⋊C4C22⋊D4311yescharacteristic
255C2×C42—862no—
256C2×C42D17211yescharacteristic
257C2×C42C22×D4311yescharacteristic
258C4⋊C8—22no—
259C4⋊C8—862no—
260C4⋊C8—862no—
261C22⋊C8—22no—
262C22⋊C8—1722no—
263C4×C8—22no—
264C24(C2×D43)⋊C411yescharacteristic
265C2×Q8—434no—
266C2×Q8—862no—
267C2×Q8—862no—
268C2×Q8—862no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—862no—
274C22×C4—862no—
275C22×C4#1062187312yes—
276C22×C4Dic17212yes—
277C22×C4(C2×D43)⋊C411yescharacteristic
278C22×C4(C2×D43)⋊C411yescharacteristic
279C22×C4(C2×D43)⋊C411yescharacteristic
280C22×C4C2×C4×D4311yescharacteristic
281C22×C4C2×D17211yescharacteristic
282C22×C4C2×C22⋊D4311yescharacteristic
283C2×C8—42no—
284C2×C8—1721no—
285C2×C8—1721no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8—1721no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—434no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C4⋊C4—864no—
296C4⋊C4—864no—
297C4⋊C4—862no—
298C4⋊C4—862no—
299C4⋊C4—864no—
300C4⋊C4—864no—
301C4⋊C4—862no—
302C4⋊C4—862no—
303C4⋊C4—862no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—864no—
307C22⋊C4—864no—
308C42—21no—
309C42—21no—
310C42—864no—
311C42—864no—
312C42D4×D4312yes—
313C42D4×D4312yes—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23#1306325012yes—
319C23C2×(C2×D43)⋊C411yescharacteristic
320Q8—3442no—
321Q8—3442no—
322Q8—3442no—
323Q8—1724no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—864no—
337C2×C4—864no—
338C2×C4—3442no—
339C2×C4—3442no—
340C2×C4#1306325012yes—
341C2×C4C22⋊C4×D4312yes—
342C2×C4#1306329312yes—
343C2×C4#1306329511yescharacteristic
344C2×C4#1306329511yescharacteristic
345C2×C4C2×#1062187311yescharacteristic
346C2×C4C2×Dic17211yescharacteristic
347C2×C4#1306335811yescharacteristic
348C2×C4#1306335811yescharacteristic
349C8—82no—
350C8—3441no—
351C8—3441no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22#1458275411yescharacteristic
360C22C2×#1306325011yescharacteristic
361C22#1458290911yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—1724no—
368C4—1724no—
369C4#1458304011yescharacteristic
370C4#1458304011yescharacteristic
371C4#1458305711yescharacteristic
372C4#1458305711yescharacteristic
373C2—21no—
374C2—21no—
375C2—42no—
376C2#1913453111yescharacteristic
377C2#1913454411yescharacteristic
378C2#1913456111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1458C2
socleC22×C43#379
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1458D43
hypocenterC43#8410
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #19133250C2semidirect
4. #19132999C2semidirect
216. C43#8410semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191345792
#191332502
#191329992
C43×#14582
#841043