Finite Group Databasebeta

← #24985391

Subgroups — #24985391

Order 11008.

492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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#19141524C211yesmaximal, characteristic
2#19135924C211yesmaximal, characteristic, complemented
3#19135923C211yesmaximal, characteristic, complemented
4#19135680C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic, complemented
8C22×#10621873—21no—
9C2×#13063325C2211yescharacteristic
10C2×#13063310—21no—
11C2×#13063259—21no—
12C2×#13063258—21no—
13C2×#13063250—21no—
14#14582832—21no—
15#14582826—21no—
16#14582825—21no—
17#14582801C2211yescharacteristic
18#14582797C2211yescharacteristic
19#14582773—21no—
20#14582770—21no—
21#14582662—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C2×#10621873—42no—
31C2×#10621873—42no—
32C2×#10621873—42no—
33C22×C43⋊C8—21no—
34#13063325—42no—
35#13063310—42no—
36#13063310—42no—
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#13063259—42no—
50#13063258—42no—
51#13063250—42no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C42×C43C2311yescharacteristic
62#95×C43—21no—
63C23×D43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—41no—
73C2×D172—21no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172D812yes—
77C2×C4×D43—42no—
78C2×C4×D43—81no—
79C2×C4×D43—81no—
80C2×Dic86—22no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×C8×C43—22no—
87C2×C8×C43—22no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C42×C43—41no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105C4⋊Dic43—22no—
106C4⋊Dic43—22no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112C4⋊Dic43—41no—
113Dic43⋊C4—41no—
114Dic43⋊C4—41no—
115Dic43⋊C4—81no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119#10621873—48no—
120C23×C43#12011yescharacteristic
121C22×D43—22no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43C2×D811yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158D172—42no—
159D172—81no—
160C4×D43—84no—
161Dic86—42no—
162Dic86—42no—
163Dic86—81no—
164Dic86—81no—
165C8×C43—42no—
166C8×C43—42no—
167C43⋊C8—42no—
168#7751—431nomaximal, Sylow
169C22×C43#44711yescharacteristic
170C22×C43#45211yescharacteristic
171C22×C43#45211yescharacteristic
172C22×C43#45311yescharacteristic
173C22×C43#45611yescharacteristic
174C22×C43#45611yescharacteristic
175C22×C43B(4,𝔽2)11yescharacteristic
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—81no—
190C4×C43—81no—
191Dic43—82no—
192Dic43—81no—
193Dic43—81no—
194Dic43—81no—
195#2724—431no—
196#2057—431no—
197#2057—431no—
198#2013—431no—
199#1271—431no—
200#1271D4311yescharacteristic, complemented
201#1270—431no—
202C2×C43#159511yescharacteristic
203C2×C43#160311yescharacteristic
204C2×C43#160311yescharacteristic
205C2×C43#163011yescharacteristic
206C2×C43#164711yescharacteristic
207C2×C43#164711yescharacteristic
208C2×C43#166011yescharacteristic
209D43—82no—
210C22×SD16—861no—
211C2×C4⋊Q8—431no—
212C2×#123—861no—
213C2×#107—861no—
214C2×#107—861no—
215C2×#103—861no—
216#398—861no—
217#397—861no—
218#397—861no—
219#390—431no—
220#389—431no—
221#389C2×D4311yescharacteristic
222#385—861no—
223#385—861no—
224#340—861no—
225#340—861no—
226#336—431no—
227#336C2×D4311yescharacteristic
228#336C2×D4311yescharacteristic
229C43#775111yescharacteristic, complemented, Sylow
230C22×Q8—861no—
231C22×D4—431no—
232C23×C4—861no—
233C2×SD16—1722no—
234C2×SD16—1722no—
235C2×SD16—1722no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—861no—
239C4⋊Q8—1722no—
240#123—1722no—
241#123—1722no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4D17211yescharacteristic
251C2×C4⋊C4D17211yescharacteristic
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C42C22×D4311yescharacteristic
258#107—1722no—
259#107—1722no—
260#103—1722no—
261#95—21no—
262#95—861no—
263#95—861no—
264#95—861no—
265#95—861no—
266C24—861no—
267C2×Q8—862no—
268C2×Q8—1721no—
269C2×Q8—1721no—
270C2×Q8—1721no—
271C2×Q8—1721no—
272C2×Q8—1721no—
273C2×D4—432no—
274C2×D4—861no—
275C2×D4—1721no—
276C2×D4—1721no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—3441no—
283C22×C4—3441no—
284C22×C4—1722no—
285C22×C4—1721no—
286C22×C4C2×D17211yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289SD16—1728no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—862no—
297C2×C8—1721no—
298C2×C8—1721no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—862no—
305C4⋊C4—862no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—3441no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C22⋊C4—1722no—
316C22⋊C4—1722no—
317C22⋊C4—1722no—
318C22⋊C4—1721no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C22⋊C4—1721no—
322C42—41no—
323C23—862no—
324C23—1721no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23—1721no—
329C23—1721no—
330C23#1306329511yescharacteristic
331Q8—3441no—
332Q8—3441no—
333Q8—1722no—
334Q8—1722no—
335D4—3441no—
336D4—1722no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—3444no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1722no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4D8×D4311yescharacteristic
363C2×C4#1306334611yescharacteristic
364C2×C4#1306334711yescharacteristic
365C2×C4#1306335211yescharacteristic
366C2×C4#1306335711yescharacteristic
367C2×C4#1306335811yescharacteristic
368C8—42no—
369C8—42no—
370C8—1722no—
371C22—3441no—
372C22—3441no—
373C22—3441no—
374C22—3441no—
375C22—1722no—
376C22—1722no—
377C22—1722no—
378C22#1458303411yescharacteristic
379C22#1458306311yescharacteristic
380C22#1458306411yescharacteristic
381C22#1458306811yescharacteristic
382C22#1458308311yescharacteristic
383C22#1458308411yescharacteristic
384C22#1458308711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—81no—
392C4—81no—
393C4—3441no—
394C4—3441no—
395C4—3442no—
396C4—3441no—
397C2—3442no—
398C2#1913351411yescharacteristic
399C2#1913356011yescharacteristic
400C2#1913356111yescharacteristic
401C2#1913371811yescharacteristic
402C2#1913383111yescharacteristic
403C2#1913383311yescharacteristic
404C2#1913390811yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1271D43
hypocenterC43#7751
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. #19135924C2semidirect
3. #19135923C2semidirect
5. #19132419C2semidirect
7. C43×#1271C2semidirect
200. #1271D43semidirect
229. C43#7751semidirect

Maximal subgroups

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

subgroupindex
#191415242
#191359242
#191359232
#191356802
#191324192
#191324152
C43×#12712
#775143