Finite Group Databasebeta

← #24993401

Subgroups — #24993401

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144067C211yesmaximal, characteristic
2#19134610C211yesmaximal, characteristic, complemented
3#19133156C211yesmaximal, characteristic
4#19132995C211yesmaximal, characteristic
5#19132491C211yesmaximal, characteristic, complemented
6#19132454C211yesmaximal, characteristic, complemented
7C43×#2983C211yesmaximal, characteristic, complemented
8C2×#13063356—21no—
9#14583449C2211yescharacteristic
10#14583121—22no—
11#14583109C412yescomplemented
12#14583099C412yescomplemented
13#14582923C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15#14582898—21no—
16C2×#13063249—21no—
17#14582765C2211yescharacteristic
18#14582661—21no—
19#14582634—22no—
20#14582628—22no—
21C2×C4×Q8×C43C2211yescharacteristic
22C43×#446—22no—
23C43×#446—22no—
24C43×#432—22no—
25C43×#431C2211yescharacteristic
26C43×#431C2211yescharacteristic
27C2×#10621898—21no—
28#13063356—42no—
29#13063356—42no—
30C2×#10621885—22no—
31C2×#10621884—22no—
32C2×#10621877—21no—
33C22×C43⋊C8—21no—
34#13063325C2×C411yescharacteristic
35#13063322C2×C411yescharacteristic
36#13063313—21no—
37#13063299—21no—
38#13063299—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C412yes—
46#13063249—42no—
47#13063248—22no—
48#13063245—22no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C22×Q8×C43D411yescharacteristic
52C4×Q8×C43—21no—
53C4×Q8×C43—21no—
54C4×Q8×C43C2×C412yes—
55C4×Q8×C43D412yes—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C42×C43—21no—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—24no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64C22⋊C8×C43D412yes—
65#97×C43—24no—
66C4×C8×C43—21no—
67C4×C8×C43D412yes—
68C2×Q8×C43—21no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43C22⋊C412yes—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—41no—
80C22×Dic43—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172—21no—
88C2×C4×D43—41no—
89C2×Dic86—21no—
90C2×C8×C43—22no—
91C2×C8×C43—22no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43C22⋊C412yes—
96C42×C43—22no—
97C42×C43—22no—
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102#10621885—44no—
103#10621884—44no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110#10621877—41no—
111#10621877—41no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C23×C43#12111yescharacteristic
117C22×D43—41no—
118Q8×C43—22no—
119Q8×C43—22no—
120Q8×C43—41no—
121Q8×C43—41no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—81no—
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12311yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C22⋊D43—81no—
140C22⋊D43—81no—
141C2×Dic43—41no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145D172—42no—
146D172—41no—
147D172—41no—
148D172—81no—
149C4×D43—81no—
150C4×D43—81no—
151Dic86—41no—
152Dic86—41no—
153C8×C43—42no—
154C8×C43—42no—
155C43⋊C8—42no—
156C43⋊C8—81no—
157#9310—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43#38611yescharacteristic
161C22×C43#46811yescharacteristic
162C22×C43#46911yescharacteristic
163C2×D43—81no—
164C2×D43—81no—
165C2×D43—81no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—42no—
171C4×C43—42no—
172C4×C43#41711yescharacteristic
173C4×C43#41811yescharacteristic
174C4×C43#46811yescharacteristic
175C4×C43#46911yescharacteristic
176Dic43—81no—
177Dic43—161no—
178#3037—431no—
179#2983D4311yescharacteristic, complemented
180#1805—431no—
181#1517—431no—
182#1480—431no—
183#1301—431no—
184#1286—431no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43#188111yescharacteristic
188C2×C43#189511yescharacteristic
189C2×C43#190511yescharacteristic
190D43—161no—
191C2×#137—861no—
192#532—431no—
193C2×C4×Q8C2×D4311yescharacteristic
194#464—862no—
195#462—432no—
196#460—432no—
197#446—22no—
198#446—22no—
199#432—22no—
200#431C2×D4311yescharacteristic
201#431C2×D4311yescharacteristic
202#423—431no—
203C2×C4⋊C8—431no—
204#417—861no—
205C2×#103—861no—
206#382—431no—
207#340—861no—
208#327—862no—
209D4⋊C8—862no—
210C43#931011yescharacteristic, complemented, Sylow
211C2×#41—861no—
212C22×Q8D17211yescharacteristic
213#137—1722no—
214#137—1722no—
215C2×Q16—862no—
216C2×SD16—862no—
217C2×M16—861no—
218C22×C8—861no—
219C4⋊Q8—431no—
220#127—431no—
221#124—861no—
222#121—861no—
223#121—861no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8C4×D4312yes—
227C4×Q8C22⋊D4312yes—
228C4×D4—861no—
229C4×D4—861no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4D17211yescharacteristic
233C2×C42—21no—
234C2×C42C22×D4311yescharacteristic
235C4⋊C8—24no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—432no—
239C4⋊C8—861no—
240C4⋊C8—861no—
241C4⋊C8—861no—
242#103—862no—
243#103—1722no—
244#102—862no—
245C22⋊C8—21no—
246C22⋊C8C22⋊D4312yes—
247#97—24no—
248C4×C8—21no—
249C4×C8C22⋊D4312yes—
250#95—861no—
251#95—861no—
252#41—1721no—
253#41—1721no—
254#41—1721no—
255#41—1721no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—861no—
262C2×Q8(C2×D43)⋊C412yes—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—1721no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1721no—
270C22×C4—1721no—
271C22×C4C2×D17211yescharacteristic
272C22×C4#1062189811yescharacteristic
273C22×C4C2×C22⋊D4311yescharacteristic
274Q16—1724no—
275SD16—1724no—
276M16—1721no—
277M16—1721no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—862no—
281C2×C8—1721no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4(C2×D43)⋊C412yes—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C42—22no—
295C42—22no—
296C42C2×C4×D4311yescharacteristic
297C42#1062189811yescharacteristic
298C42C2×C22⋊D4311yescharacteristic
299C42C2×C22⋊D4311yescharacteristic
300C23—1721no—
301C23#1306329911yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—41no—
305Q8—41no—
306Q8—1721no—
307Q8—1721no—
308D4—3441no—
309D4—3441no—
310D4—3441no—
311D4—1722no—
312D4—1721no—
313D4—1721no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—3441no—
325C2×C4—3441no—
326C2×C4—1721no—
327C2×C4C2×(C2×D43)⋊C411yescharacteristic
328C2×C4C4×C22⋊D4311yescharacteristic
329C2×C4C4×C22⋊D4311yescharacteristic
330C2×C4#1306329411yescharacteristic
331C2×C4#1306329911yescharacteristic
332C2×C4#1306330811yescharacteristic
333C2×C4#1306335311yescharacteristic
334C2×C4#1306335311yescharacteristic
335C2×C4#1306335311yescharacteristic
336C2×C4#1306335811yescharacteristic
337C8—42no—
338C8—42no—
339C8—3441no—
340C8—1722no—
341C22—21no—
342C22—21no—
343C22—3441no—
344C22—3441no—
345C22—3441no—
346C22#1458277811yescharacteristic
347C22#1458314511yescharacteristic
348C22#1458315211yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—42no—
355C4—3441no—
356C4—6881no—
357C4#1458290111yescharacteristic
358C4#1458290511yescharacteristic
359C4#1458314511yescharacteristic
360C4#1458315211yescharacteristic
361C2—21no—
362C2—21no—
363C2—6881no—
364C2#1913495711yescharacteristic
365C2#1913503311yescharacteristic
366C2#1913508911yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2983C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2983D43
hypocenterC43#9310
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #19134610C2semidirect
5. #19132491C2semidirect
6. #19132454C2semidirect
7. C43×#2983C2semidirect
11. #14583109C4semidirect
12. #14583099C4semidirect
179. #2983D43semidirect
210. C43#9310semidirect

Maximal subgroups

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

subgroupindex
#191440672
#191346102
#191331562
#191329952
#191324912
#191324542
C43×#29832
#931043