Finite Group Databasebeta

← #24992525

Subgroups — #24992525

Order 11008.

446 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#19144400C211yesmaximal, characteristic
2#19133158C211yesmaximal, characteristic
3#19133093C211yesmaximal, characteristic
4#19132990C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic
6#19132453C211yesmaximal, characteristic
7C43×#2356C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583206—22no—
10#14583194C412yescomplemented
11#14583184C412yescomplemented
12#14582952C2211yescharacteristic
13#14582952C2211yescharacteristic
14#14582939—21no—
15#14582923C2211yescharacteristic
16#14582908—21no—
17#14582635—21no—
18#14582635—21no—
19#14582635—22no—
20Q8⋊(C43⋊C8)—22no—
21C2×C4×Q8×C43C2211yescharacteristic
22C43×#391—21no—
23C43×#387—22no—
24C43×#383—21no—
25C43×#382C2211yescharacteristic
26C4×C4⋊C4×C43—21no—
27C4×C4⋊C4×C43C2211yescharacteristic
28C43×#376—21no—
29C2×#10621877—21no—
30#13063325C2×C411yescharacteristic
31#13063325C2×C411yescharacteristic
32#13063317—21no—
33#13063304—21no—
34#13063304—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37#13063284—21no—
38#13063258—22no—
39#13063256—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C412yes—
44#13063249—22no—
45#13063249—22no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C22×Q8×C43D411yescharacteristic
51C4×Q8×C43—21no—
52C4×Q8×C43—21no—
53C4×Q8×C43C2×C412yes—
54C4×Q8×C43D412yes—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C42×C43—21no—
60C2×C42×C43—22no—
61C2×C42×C43—21no—
62C2×C42×C43C2311yescharacteristic
63#95×C43—22no—
64#95×C43—22no—
65#95×C43—22no—
66#95×C43—21no—
67#95×C43D411yescharacteristic
68#95×C43D411yescharacteristic
69#95×C43D412yes—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43C22⋊C412yes—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C2×Dic86—21no—
85C2×Dic86—21no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—42no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43C22⋊C412yes—
93C42×C43—22no—
94C42×C43—22no—
95C42×C43—44no—
96C42×C43—41no—
97C42×C43—41no—
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101C42×C43#4111yescharacteristic
102C22⋊Dic43—41no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C4×Dic43—41no—
110#10621877—41no—
111#10621877—41no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C23×C43#12011yescharacteristic
116Q8×C43—22no—
117Q8×C43—22no—
118Q8×C43—41no—
119Q8×C43—41no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12311yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43#13511yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C2×Dic43—41no—
147C2×Dic43—41no—
148Dic86—81no—
149Dic86—81no—
150C43⋊C8—42no—
151C43⋊C8—81no—
152C43⋊C8—81no—
153#9178—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#38611yescharacteristic
157C22×C43#45211yescharacteristic
158C22×C43#45211yescharacteristic
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—42no—
164C4×C43—42no—
165C4×C43—42no—
166C4×C43—81no—
167C4×C43—82no—
168C4×C43#41611yescharacteristic
169C4×C43#41911yescharacteristic
170C4×C43#48511yescharacteristic
171C4×C43#48511yescharacteristic
172Dic43—81no—
173Dic43—81no—
174#3078—431no—
175#2356D4311yescharacteristic
176#1518—431no—
177#1503—431no—
178#1479—431no—
179#1303—431no—
180#1286—431no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43#187311yescharacteristic
184C2×C43#190511yescharacteristic
185C2×C43#190611yescharacteristic
186#533—431no—
187C2×C4×Q8C2×D4311yescharacteristic
188#479—862no—
189#477—432no—
190#475—432no—
191#431—431no—
192#431—431no—
193#428—861no—
194#423—431no—
195#419—861no—
196#391—21no—
197#387—22no—
198#383—21no—
199#382C2×D4311yescharacteristic
200C4×C4⋊C4—21no—
201C4×C4⋊C4C2×D4311yescharacteristic
202#376—21no—
203#328—861no—
204#328—861no—
205#328—862no—
206Q8⋊C8—862no—
207C43#917811yescharacteristic, complemented, Sylow
208C22×Q8C22⋊D4311yescharacteristic
209C2×M16—861no—
210C4⋊Q8—431no—
211C4⋊Q8—431no—
212#125—861no—
213C22⋊Q8—861no—
214C22⋊Q8—861no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—861no—
218C4×Q8—861no—
219C4×Q8C4×D4312yes—
220C4×Q8D17212yes—
221#117—861no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C22⋊D4311yescharacteristic
226C2×C42—21no—
227C2×C42—22no—
228C2×C42—21no—
229C2×C42C22×D4311yescharacteristic
230#107—862no—
231#106—862no—
232C4⋊C8—432no—
233C4⋊C8—861no—
234C4⋊C8—861no—
235C4⋊C8—861no—
236#103—862no—
237#103—862no—
238C22⋊C8—861no—
239C22⋊C8—861no—
240C4×C8—861no—
241C4×C8—861no—
242#95—22no—
243#95—22no—
244#95—22no—
245#95—21no—
246#95C22⋊D4311yescharacteristic
247#95C22⋊D4311yescharacteristic
248#95C22⋊D4312yes—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—861no—
255C2×Q8—861no—
256C2×Q8(C2×D43)⋊C412yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4C2×C22⋊D4311yescharacteristic
263C22×C4C2×C22⋊D4311yescharacteristic
264C22×C4C2×C22⋊D4311yescharacteristic
265M16—1721no—
266M16—1721no—
267C2×C8—862no—
268C2×C8—1721no—
269C2×C8—1721no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—42no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4(C2×D43)⋊C412yes—
283C22⋊C4—1721no—
284C42—22no—
285C42—22no—
286C42—44no—
287C42—41no—
288C42—41no—
289C42—1721no—
290C42C2×C4×D4311yescharacteristic
291C42C2×D17211yescharacteristic
292C42#1062189811yescharacteristic
293C42#1062189811yescharacteristic
294C23#1306329411yescharacteristic
295Q8—22no—
296Q8—22no—
297Q8—41no—
298Q8—41no—
299Q8—3441no—
300Q8—3441no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4C2×(C2×D43)⋊C411yescharacteristic
320C2×C4C4×C22⋊D4311yescharacteristic
321C2×C4C4×C22⋊D4311yescharacteristic
322C2×C4#1306329911yescharacteristic
323C2×C4#1306329911yescharacteristic
324C2×C4#1306330811yescharacteristic
325C2×C4#1306334511yescharacteristic
326C2×C4#1306334511yescharacteristic
327C2×C4#1306335511yescharacteristic
328C2×C4#1306335511yescharacteristic
329C8—3441no—
330C8—3441no—
331C8—1722no—
332C22—21no—
333C22—21no—
334C22#1458277811yescharacteristic
335C22#1458306111yescharacteristic
336C22#1458306111yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—42no—
343C4—42no—
344C4—81no—
345C4—82no—
346C4—3441no—
347C4—3441no—
348C4#1458289311yescharacteristic
349C4#1458290711yescharacteristic
350C4#1458324011yescharacteristic
351C4#1458324011yescharacteristic
352C2—21no—
353C2—21no—
354C2#1913490711yescharacteristic
355C2#1913508911yescharacteristic
356C2#1913509611yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2356C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2356D43
hypocenterC43#9178
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
10. #14583194C4semidirect
11. #14583184C4semidirect
207. C43#9178semidirect

Maximal subgroups

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

subgroupindex
#191444002
#191331582
#191330932
#191329902
#191324982
#191324532
C43×#23562
#917843