Finite Group Databasebeta

← #24985469

Subgroups — #24985469

Order 11008.

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

normal subgroups only

This group has 504 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#19135923C211yesmaximal, characteristic, complemented
3#19135842C211yesmaximal, characteristic, complemented
4#19135732C211yesmaximal, characteristic
5#19132417C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×#13063305—21no—
10C2×#13063303—21no—
11C2×#13063258—21no—
12C2×#13063250—21no—
13C2×#13063250—21no—
14C2×#13063247—21no—
15#14582821—21no—
16#14582821—21no—
17#14582820—21no—
18#14582801C2211yescharacteristic
19#14582797C2211yescharacteristic
20#14582777—21no—
21#14582662—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×Dic86—21no—
29C22×D172D411yescharacteristic
30C22×C4×D43—21no—
31C22×C43⋊C8—21no—
32#13063325—42no—
33#13063305—42no—
34#13063305—42no—
35#13063303—42no—
36#13063303—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×C4⋊Dic43D411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50#13063258—42no—
51#13063250—42no—
52#13063250—42no—
53#13063247—42no—
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×D172Q1612yes—
77C2×C4×D43—42no—
78C2×C4×D43—42no—
79C2×C4×D43—81no—
80C2×Dic86—22no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—42no—
86C2×Dic86—42no—
87C2×Dic86—41no—
88C2×Dic86—81no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43SD1612yes—
100C42×C43—41no—
101(C2×D43)⋊C4—42no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—81no—
108C4⋊Dic43—21no—
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43—42no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116C4⋊Dic43D812yes—
117Dic43⋊C4—42no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C23×C43#12011yescharacteristic
124C22×D43—22no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—41no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43C2×D811yescharacteristic
144C2×C4×C43C2×SD1611yescharacteristic
145C2×C4×C43C2×Q1611yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C43#13711yescharacteristic
149C2×Dic43—22no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—42no—
158C2×Dic43—41no—
159C2×Dic43—81no—
160C2×Dic43—81no—
161D172—42no—
162D172—81no—
163C4×D43—84no—
164Dic86—42no—
165Dic86—42no—
166Dic86—84no—
167Dic86—81no—
168Dic86—81no—
169C8×C43—81no—
170C8×C43—81no—
171C43⋊C8—42no—
172#7764—431nomaximal, Sylow
173C22×C43#44711yescharacteristic
174C22×C43#45011yescharacteristic
175C22×C43#45111yescharacteristic
176C22×C43#45411yescharacteristic
177C22×C43#45511yescharacteristic
178C22×C43#45611yescharacteristic
179C22×C43B(4,𝔽2)11yescharacteristic
180C2×D43—42no—
181C2×D43—42no—
182C2×D43—42no—
183C2×D43—81no—
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—42no—
194C4×C43—81no—
195Dic43—42no—
196Dic43—82no—
197Dic43—81no—
198Dic43—81no—
199#2683—431no—
200#2057—431no—
201#2043—431no—
202#2023—431no—
203#1271—431no—
204#1271D4311yescharacteristic, complemented
205#1270—431no—
206C2×C43#159811yescharacteristic
207C2×C43#160211yescharacteristic
208C2×C43#160411yescharacteristic
209C2×C43#163711yescharacteristic
210C2×C43#163911yescharacteristic
211C2×C43#164911yescharacteristic
212C2×C43#166411yescharacteristic
213D43—82no—
214C2×C4⋊Q8—431no—
215C2×C22⋊Q8—861no—
216C2×C22⋊Q8—861no—
217C2×#107—861no—
218C2×#103—861no—
219C2×#103—861no—
220C2×#102—861no—
221#396—861no—
222#396—861no—
223#395—861no—
224#390—431no—
225#389—431no—
226#389C2×D4311yescharacteristic
227#386—861no—
228#340—861no—
229#340—861no—
230#336—431no—
231#336C2×D4311yescharacteristic
232#336C2×D4311yescharacteristic
233C43#776411yescharacteristic, complemented, Sylow
234C22×Q8—861no—
235C22×Q8—861no—
236C22×D4—431no—
237C23×C4—861no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—861no—
241C4⋊Q8—1722no—
242C22⋊Q8—1722no—
243C22⋊Q8—1722no—
244C22⋊Q8—1722no—
245C22⋊Q8—1722no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4D17211yescharacteristic
256C2×C4⋊C4D17211yescharacteristic
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C42C22×D4311yescharacteristic
263#107—1722no—
264#103—1722no—
265#103—1722no—
266#102—1722no—
267#95—21no—
268#95—861no—
269#95—861no—
270C24—861no—
271C2×Q8—862no—
272C2×Q8—3441no—
273C2×Q8—1721no—
274C2×Q8—1721no—
275C2×Q8—1722no—
276C2×Q8—1721no—
277C2×Q8—1722no—
278C2×Q8—1721no—
279C2×Q8—1721no—
280C2×D4—432no—
281C2×D4—861no—
282C2×D4—1721no—
283C2×D4—1721no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—3441no—
290C22×C4—1722no—
291C22×C4—1722no—
292C22×C4—1721no—
293C22×C4C2×D17211yescharacteristic
294C22×C4D4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—862no—
303C2×C8—1721no—
304C2×C8—1721no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—432no—
310C4⋊C4—862no—
311C4⋊C4—862no—
312C4⋊C4—861no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4—1722no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C4⋊C4—1722no—
319C4⋊C4—1721no—
320C4⋊C4—1721no—
321C4⋊C4#1062187312yes—
322C22⋊C4—3441no—
323C22⋊C4—1722no—
324C22⋊C4—1722no—
325C22⋊C4—1721no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C22⋊C4—1721no—
329C42—41no—
330C23—862no—
331C23—1721no—
332C23—1721no—
333C23—1721no—
334C23—1721no—
335C23—1721no—
336C23—1721no—
337C23#1306329511yescharacteristic
338Q8—3441no—
339Q8—3441no—
340Q8—3444no—
341Q8—1722no—
342Q8—1722no—
343D4—3441no—
344D4—1722no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—862no—
358C2×C4—3444no—
359C2×C4—3441no—
360C2×C4—3441no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1722no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4D8×D4311yescharacteristic
371C2×C4C2×#1062187311yescharacteristic
372C2×C4Q16×D4311yescharacteristic
373C2×C4#1306335211yescharacteristic
374C2×C4#1306335311yescharacteristic
375C2×C4#1306335411yescharacteristic
376C8—81no—
377C8—81no—
378C8—1722no—
379C22—3441no—
380C22—3441no—
381C22—3441no—
382C22—3441no—
383C22—1722no—
384C22—1722no—
385C22—1722no—
386C22#1458303411yescharacteristic
387C22#1458305211yescharacteristic
388C22#1458305611yescharacteristic
389C22#1458307311yescharacteristic
390C22#1458307811yescharacteristic
391C22#1458308411yescharacteristic
392C22#1458308711yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—81no—
401C4—3441no—
402C4—3442no—
403C4—3441no—
404C4—1722no—
405C2—3442no—
406C2#1913353111yescharacteristic
407C2#1913355311yescharacteristic
408C2#1913356611yescharacteristic
409C2#1913376211yescharacteristic
410C2#1913377711yescharacteristic
411C2#1913384511yescharacteristic
412C2#1913393111yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1271D43
hypocenterC43#7764
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. #19135923C2semidirect
3. #19135842C2semidirect
5. #19132417C2semidirect
7. C43×#1271C2semidirect
204. #1271D43semidirect
233. C43#7764semidirect

Maximal subgroups

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

subgroupindex
#191409662
#191359232
#191358422
#191357322
#191324172
#191324152
C43×#12712
#776443