Finite Group Databasebeta

← #24985657

Subgroups — #24985657

Order 11008.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#19140966C211yesmaximal, characteristic
2#19136153C211yesmaximal, characteristic, complemented
3#19136073C211yesmaximal, characteristic, complemented
4#19136000C211yesmaximal, characteristic
5#19132417C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063305—21no—
9C2×#13063303—21no—
10C2×#13063257—21no—
11C2×#13063247—21no—
12#14582821—21no—
13#14582821—21no—
14#14582820—21no—
15#14582801C2211yescharacteristic
16#14582797C2211yescharacteristic
17#14582777—21no—
18#14582769C2211yescharacteristic
19#14582662—21no—
20#14582662—21no—
21#14582661—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C22×C43⋊C8—21no—
31#13063305—42no—
32#13063305—42no—
33#13063303—42no—
34#13063303—42no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49#13063257—42no—
50#13063247—42no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C22×C8×C43—21no—
54C22×C8×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#95×C43—21no—
60C23×D43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—41no—
70C2×D172—21no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172SD1612yes—
74C2×C4×D43—42no—
75C2×C4×D43—42no—
76C2×C4×D43—81no—
77C2×Dic86—42no—
78C2×Dic86—42no—
79C2×Dic86—81no—
80C2×C8×C43—22no—
81C2×C8×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43SD1612yes—
91C42×C43—41no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—81no—
99C4⋊Dic43—21no—
100C4⋊Dic43—42no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103C4⋊Dic43—42no—
104C4⋊Dic43—41no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43D812yes—
109Dic43⋊C4—42no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C23×C43#12011yescharacteristic
116C22×D43—22no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43C2×D811yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43C2×SD1611yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×Dic43—22no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153D172—42no—
154D172—81no—
155C4×D43—84no—
156Dic86—84no—
157C8×C43—42no—
158C8×C43—81no—
159C43⋊C8—81no—
160#7791—431nomaximal, Sylow
161C22×C43#44711yescharacteristic
162C22×C43#44811yescharacteristic
163C22×C43#45011yescharacteristic
164C22×C43#45411yescharacteristic
165C22×C43#45511yescharacteristic
166C22×C43#45611yescharacteristic
167C22×C43#45811yescharacteristic
168C2×D43—42no—
169C2×D43—42no—
170C2×D43—42no—
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43—81no—
183Dic43—42no—
184Dic43—81no—
185Dic43—81no—
186Dic43—161no—
187#2683—431no—
188#2099—431no—
189#2084—431no—
190#2071—431no—
191#1271—431no—
192#1271D4311yescharacteristic, complemented
193#1270—431no—
194C2×C43#160811yescharacteristic
195C2×C43#161011yescharacteristic
196C2×C43#161611yescharacteristic
197C2×C43#162711yescharacteristic
198C2×C43#163911yescharacteristic
199C2×C43#165111yescharacteristic
200C2×C43#166411yescharacteristic
201D43—82no—
202C2×C22⋊Q8—861no—
203C2×C22⋊Q8—861no—
204C2×#106—861no—
205C2×#102—861no—
206#396—861no—
207#396—861no—
208#395—861no—
209#390—431no—
210#389—431no—
211#389C2×D4311yescharacteristic
212#386—861no—
213#384—431no—
214#340—861no—
215#340—861no—
216#340—861no—
217#340—861no—
218#336—431no—
219#336C2×D4311yescharacteristic
220#336C2×D4311yescharacteristic
221C43#779111yescharacteristic, complemented, Sylow
222C22×Q8—861no—
223C22×D4—431no—
224C23×C4—861no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—861no—
228C22⋊Q8—1722no—
229C22⋊Q8—1722no—
230C22⋊Q8—1722no—
231C22⋊Q8—1722no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4D17211yescharacteristic
243C2×C4⋊C4D17211yescharacteristic
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C42C22×D4311yescharacteristic
250#106—1722no—
251#102—1722no—
252#95—21no—
253#95—861no—
254#95—861no—
255C24—861no—
256C2×Q8—3441no—
257C2×Q8—1722no—
258C2×Q8—1722no—
259C2×D4—432no—
260C2×D4—861no—
261C2×D4—1721no—
262C2×D4—1721no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—3441no—
269C22×C4—1722no—
270C22×C4—1722no—
271C22×C4—1721no—
272C22×C4C2×D17211yescharacteristic
273C22×C4D4×D4311yescharacteristic
274C22×C4D4×D4311yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—1721no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—432no—
289C4⋊C4—861no—
290C4⋊C4—1722no—
291C4⋊C4—1721no—
292C4⋊C4—1721no—
293C4⋊C4—1722no—
294C4⋊C4—1722no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C4⋊C4#1062187312yes—
302C22⋊C4—3441no—
303C22⋊C4—1722no—
304C22⋊C4—1722no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C42—41no—
310C23—862no—
311C23—1721no—
312C23—1721no—
313C23—1721no—
314C23—1721no—
315C23—1721no—
316C23—1721no—
317C23#1306329511yescharacteristic
318Q8—3444no—
319D4—3441no—
320D4—1722no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—862no—
334C2×C4—3444no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4D8×D4311yescharacteristic
347C2×C4SD16×D4311yescharacteristic
348C2×C4C2×#1062187311yescharacteristic
349C2×C4#1306335211yescharacteristic
350C2×C4#1306335311yescharacteristic
351C2×C4#1306335711yescharacteristic
352C8—42no—
353C8—81no—
354C8—3441no—
355C22—3441no—
356C22—3441no—
357C22—3441no—
358C22—3441no—
359C22—1722no—
360C22—1722no—
361C22—1722no—
362C22#1458303411yescharacteristic
363C22#1458303911yescharacteristic
364C22#1458305211yescharacteristic
365C22#1458307411yescharacteristic
366C22#1458307811yescharacteristic
367C22#1458308311yescharacteristic
368C22#1458309011yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—3441no—
378C4—3441no—
379C4—1722no—
380C4—6881no—
381C2—3442no—
382C2#1913358711yescharacteristic
383C2#1913359911yescharacteristic
384C2#1913363411yescharacteristic
385C2#1913369911yescharacteristic
386C2#1913377711yescharacteristic
387C2#1913386111yescharacteristic
388C2#1913393011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1271D43
hypocenterC43#7791
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #19136153C2semidirect
3. #19136073C2semidirect
5. #19132417C2semidirect
7. C43×#1271C2semidirect
192. #1271D43semidirect
221. C43#7791semidirect

Maximal subgroups

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

subgroupindex
#191409662
#191361532
#191360732
#191360002
#191324172
#191324152
C43×#12712
#779143