Finite Group Databasebeta

← #24985535

Subgroups — #24985535

Order 11008.

472 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 85 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#19141613C211yesmaximal, characteristic
2#19135838C211yesmaximal, characteristic, complemented
3#19135728C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic, complemented
5#19132419C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2024C211yesmaximal, characteristic, complemented
8C2×#13063301—21no—
9C2×#13063249—21no—
10C2×#13063249—21no—
11C2×#13063245—21no—
12#14582836—21no—
13#14582831—21no—
14#14582821—21no—
15#14582801C2211yescharacteristic
16#14582797C2211yescharacteristic
17#14582777—21no—
18#14582773—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#103×C43—21no—
24C43×#391C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×D172D411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063301—42no—
32#13063301—42no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4⋊Dic43D411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45#13063249—42no—
46#13063249—42no—
47#13063245—42no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×Q8×C43—21no—
51C22×Q8×C43D411yescharacteristic
52C22×C8×C43—21no—
53C4⋊Q8×C43—42no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#103×C43—42no—
59#95×C43—21no—
60#95×C43—21no—
61C23×D43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—22no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43SD1612yes—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C2×D172—21no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172Q1612yes—
85C2×C4×D43—42no—
86C2×C4×D43—81no—
87C2×C4×D43—81no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C42×C43—41no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—81no—
103(C2×D43)⋊C4—81no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—42no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C4⋊Dic43—81no—
110Dic43⋊C4—42no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C23×C43#12011yescharacteristic
120C22×D43—22no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127Q8×C43—42no—
128Q8×C43—42no—
129Q8×C43—42no—
130Q8×C43—81no—
131Q8×C43—81no—
132Q8×C43—81no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—22no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43C2×SD1611yescharacteristic
149C2×C4×C43C2×Q1611yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43#13711yescharacteristic
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163D172—42no—
164D172—81no—
165C4×D43—84no—
166C8×C43—81no—
167C43⋊C8—81no—
168C43⋊C8—81no—
169#7774—431nomaximal, Sylow
170C22×C43#44911yescharacteristic
171C22×C43#45011yescharacteristic
172C22×C43#45111yescharacteristic
173C22×C43#45411yescharacteristic
174C22×C43#45511yescharacteristic
175C22×C43#45511yescharacteristic
176C22×C43B(4,𝔽2)11yescharacteristic
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—42no—
191C4×C43—82no—
192C4×C43—81no—
193Dic43—81no—
194Dic43—81no—
195Dic43—81no—
196#2732—431no—
197#2043—431no—
198#2024D4311yescharacteristic, complemented
199#2023—431no—
200#1272—431no—
201#1271—431no—
202#1270—431no—
203C2×C43#159711yescharacteristic
204C2×C43#160111yescharacteristic
205C2×C43#160211yescharacteristic
206C2×C43#163711yescharacteristic
207C2×C43#164211yescharacteristic
208C2×C43#164411yescharacteristic
209C2×C43#166211yescharacteristic
210D43—82no—
211C2×C4⋊Q8C2×D4311yescharacteristic
212C2×C22⋊Q8—861no—
213C2×#103—21no—
214C2×#103—861no—
215C2×#103—861no—
216C2×#102—861no—
217#399—861no—
218#398—861no—
219#396—861no—
220#391C2×D4311yescharacteristic
221#390—431no—
222#389—431no—
223#386—861no—
224#385—861no—
225#340—21no—
226#340—861no—
227#336—431no—
228#336—431no—
229#336C2×D4311yescharacteristic
230C43#777411yescharacteristic, complemented, Sylow
231C22×Q8—21no—
232C22×Q8C22⋊D4311yescharacteristic
233C22×D4—431no—
234C23×C4—861no—
235C22×C8—21no—
236C22×C8—861no—
237C22×C8—861no—
238C4⋊Q8—42no—
239C22⋊Q8—1722no—
240C22⋊Q8—1722no—
241C2×C4⋊C4—21no—
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⋊C4C22⋊D4311yescharacteristic
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C42C22×D4311yescharacteristic
257#103—42no—
258#103—1722no—
259#103—1722no—
260#102—1722no—
261#95—21no—
262#95—21no—
263#95—861no—
264#95—861no—
265C24—861no—
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8#1062188412yes—
276C2×D4—432no—
277C2×D4—861no—
278C2×D4—1721no—
279C2×D4—1721no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—3441no—
287C22×C4—3441no—
288C22×C4—1722no—
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—1721no—
296C2×C8—1721no—
297C2×C8—1721no—
298C2×C8—1721no—
299C2×C8—1721no—
300C2×C8—1721no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—3441no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4—1722no—
312C4⋊C4—1722no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C22⋊C4—3441no—
316C22⋊C4—3441no—
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#1306329311yescharacteristic
331Q8—42no—
332Q8—42no—
333Q8—42no—
334Q8—81no—
335Q8—81no—
336Q8—81no—
337D4—3441no—
338D4—1722no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—3444no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4C2×#1062188411yescharacteristic
365C2×C4Q16×D4311yescharacteristic
366C2×C4#1306334611yescharacteristic
367C2×C4#1306335011yescharacteristic
368C2×C4#1306335211yescharacteristic
369C2×C4#1306335711yescharacteristic
370C8—81no—
371C8—3441no—
372C8—3441no—
373C22—3441no—
374C22—3441no—
375C22—3441no—
376C22—3441no—
377C22—1722no—
378C22—1722no—
379C22—1722no—
380C22#1458304311yescharacteristic
381C22#1458304911yescharacteristic
382C22#1458305311yescharacteristic
383C22#1458307011yescharacteristic
384C22#1458307511yescharacteristic
385C22#1458307611yescharacteristic
386C22#1458308511yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4—3441no—
397C4—3441no—
398C4—3441no—
399C2—3442no—
400C2#1913352311yescharacteristic
401C2#1913354611yescharacteristic
402C2#1913355011yescharacteristic
403C2#1913375811yescharacteristic
404C2#1913379411yescharacteristic
405C2#1913380611yescharacteristic
406C2#1913391711yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2024C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2024D43
hypocenterC43#7774
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. #19135838C2semidirect
4. #19132421C2semidirect
5. #19132419C2semidirect
7. C43×#2024C2semidirect
198. #2024D43semidirect
230. C43#7774semidirect

Maximal subgroups

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

subgroupindex
#191416132
#191358382
#191357282
#191324212
#191324192
#191324152
C43×#20242
#777443