Finite Group Databasebeta

← #24992883

Subgroups — #24992883

Order 11008.

474 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#19144634C211yesmaximal, characteristic
2#19135572C211yesmaximal, characteristic
3#19133093C211yesmaximal, characteristic
4#19133024C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic
6#19132428C211yesmaximal, characteristic
7C43×#2295C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583234—21no—
10#14583194C412yescomplemented
11#14583109C412yescomplemented
12#14583055—21no—
13C4×#10621885—22no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16#14582923C2211yescharacteristic
17#14582659—21no—
18#14582659—21no—
19#14582635—22no—
20Q8⋊(C43⋊C8)—22no—
21C2×C4×Q8×C43C2211yescharacteristic
22C43×#391—21no—
23C43×#389—21no—
24C43×#387—22no—
25C4×C4⋊C4×C43—21no—
26C4×C4⋊C4×C43C2211yescharacteristic
27C43×#376—21no—
28C43×C43C2211yescharacteristic
29C2×#10621885—22no—
30C2×#10621877—21no—
31#13063325C2×C411yescharacteristic
32#13063325C2×C411yescharacteristic
33#13063317—21no—
34#13063304—21no—
35#13063304—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38#13063284—21no—
39#13063258—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C412yes—
44#13063249—22no—
45#13063248—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—22no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C42×C43—21no—
60C2×C42×C43—21no—
61C2×C42×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43D411yescharacteristic
64C2×C42×C43D411yescharacteristic
65C2×C42×C43C2311yescharacteristic
66#95×C43—22no—
67#95×C43—22no—
68#95×C43—22no—
69#95×C43D412yes—
70C2×Q8×C43—21no—
71C2×Q8×C43—42no—
72C2×Q8×C43C22⋊C412yes—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—22no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C2×Dic86—21no—
82C2×Dic86—21no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—44no—
88C4⋊C4×C43C22⋊C412yes—
89C42×C43—22no—
90C42×C43—22no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43—21no—
94C42×C43—42no—
95C42×C43—42no—
96C42×C43—41no—
97C42×C43—41no—
98C42×C43Q1612yescomplemented
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102C42×C43#4111yescharacteristic
103C22⋊Dic43—41no—
104#10621885—44no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111C4×Dic43—41no—
112#10621877—41no—
113#10621877—41no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43#12011yescharacteristic
118Q8×C43—22no—
119Q8×C43—22no—
120Q8×C43—42no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
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×C43C2×Q1611yescharacteristic
143C2×C4×C43#13511yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C2×Dic43—41no—
147C2×Dic43—41no—
148Dic86—42no—
149Dic86—81no—
150C43⋊C8—42no—
151C43⋊C8—81no—
152C43⋊C8—81no—
153#9236—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#38611yescharacteristic
157C22×C43#45111yescharacteristic
158C22×C43#45211yescharacteristic
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—42no—
163C4×C43—42no—
164C4×C43—42no—
165C4×C43—42no—
166C4×C43—82no—
167C4×C43#42112yes—
168C4×C43C4×Q1611yescharacteristic
169C4×C43#44111yescharacteristic
170C4×C43#46211yescharacteristic
171C4×C43#46411yescharacteristic
172Dic43—81no—
173Dic43—81no—
174#3104—431no—
175#2295D4311yescharacteristic
176#1994—431no—
177#1503—431no—
178#1487—431no—
179#1303—431no—
180#1276—431no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43#187811yescharacteristic
184C2×C43#189711yescharacteristic
185C2×C43#190611yescharacteristic
186#533—431no—
187C2×C4×Q8C2×D4311yescharacteristic
188#484—861no—
189#477—432no—
190#462—432no—
191#451—861no—
192C4×Q16—862no—
193#431—431no—
194#431—431no—
195#423—431no—
196#391—21no—
197#389—21no—
198#387—22no—
199C4×C4⋊C4—21no—
200C4×C4⋊C4C2×D4311yescharacteristic
201#376—21no—
202C43C2×D4311yescharacteristic
203#339—861no—
204#339—861no—
205#328—862no—
206Q8⋊C8—862no—
207C43#923611yescharacteristic, complemented, Sylow
208C22×Q8C22⋊D4311yescharacteristic
209C2×Q16—862no—
210C2×M16—861no—
211C4⋊Q8—431no—
212C4⋊Q8—431no—
213#125—861no—
214C22⋊Q8—861no—
215C22⋊Q8—861no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—861no—
219C4×Q8—861no—
220C4×Q8C4×D4312yes—
221C4×Q8D17212yes—
222#117—861no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D4311yescharacteristic
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42C22⋊D4311yescharacteristic
232C2×C42C22⋊D4311yescharacteristic
233C2×C42C22×D4311yescharacteristic
234#107—862no—
235C4⋊C8—432no—
236C4⋊C8—861no—
237C4⋊C8—861no—
238C4⋊C8—861no—
239#103—862no—
240#103—862no—
241C22⋊C8—861no—
242C22⋊C8—861no—
243C4×C8—861no—
244C4×C8—861no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95C22⋊D4312yes—
249C2×Q8—21no—
250C2×Q8—42no—
251C2×Q8—861no—
252C2×Q8—861no—
253C2×Q8(C2×D43)⋊C412yes—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4C2×C22⋊D4311yescharacteristic
260C22×C4C2×C22⋊D4311yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262Q16—1724no—
263M16—1721no—
264M16—1721no—
265C2×C8—862no—
266C2×C8—1721no—
267C2×C8—1721no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—42no—
272C4⋊C4—44no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4(C2×D43)⋊C412yes—
280C22⋊C4—1721no—
281C42—22no—
282C42—22no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—42no—
287C42—42no—
288C42—41no—
289C42—41no—
290C42—1721no—
291C42#1062188512yescomplemented
292C42C2×C4×D4311yescharacteristic
293C42C2×D17211yescharacteristic
294C42#1062189811yescharacteristic
295C42#1062189811yescharacteristic
296C23#1306329411yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—42no—
300Q8—3441no—
301Q8—1722no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
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×C4C2×#1062188511yescharacteristic
326C2×C4#1306334511yescharacteristic
327C2×C4#1306335511yescharacteristic
328C2×C4#1306335611yescharacteristic
329C8—3441no—
330C8—3441no—
331C8—1722no—
332C22—21no—
333C22—21no—
334C22#1458277811yescharacteristic
335C22#1458305511yescharacteristic
336C22#1458306111yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—42no—
344C4—82no—
345C4—3441no—
346C4—3441no—
347C4#1458291712yes—
348C4C4×#1062188511yescharacteristic
349C4#1458300411yescharacteristic
350C4#1458310911yescharacteristic
351C4#1458312111yescharacteristic
352C2—21no—
353C2—21no—
354C2#1913493611yescharacteristic
355C2#1913504311yescharacteristic
356C2#1913509611yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2295C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2295D43
hypocenterC43#9236
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2295

Complements

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

NH ≅ G/Ntype
10. #14583194C4semidirect
11. #14583109C4semidirect
98. C42×C43Q16semidirect
207. C43#9236semidirect
291. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191446342
#191355722
#191330932
#191330242
#191324982
#191324282
C43×#22952
#923643