Finite Group Databasebeta

← #24985646

Subgroups — #24985646

Order 11008.

516 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140958C211yesmaximal, characteristic
2#19136067C211yesmaximal, characteristic, complemented
3#19135999C211yesmaximal, characteristic, complemented
4#19132417C211yesmaximal, characteristic, complemented
5#19132416C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic, complemented
7C43×#2093C211yesmaximal, characteristic, complemented
8C2×#13063307—21no—
9C2×#13063298—21no—
10C2×#13063258—21no—
11C2×#13063245—21no—
12#14582822—21no—
13#14582815—21no—
14#14582807—21no—
15#14582801C2211yescharacteristic
16#14582797C2211yescharacteristic
17#14582770—21no—
18#14582661—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×#107×C43—21no—
23C2×#102×C43—21no—
24C43×#390C2211yescharacteristic
25C43×#384C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×D172D411yescharacteristic
28C22×C22⋊D43—21no—
29C22×C22⋊D43—21no—
30C22×C4×D43—21no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33#13063307—42no—
34#13063307—42no—
35#13063298—42no—
36#13063298—42no—
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47#13063258—42no—
48#13063245—42no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C22×D4×C43D411yescharacteristic
52C22×C8×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43C2311yescharacteristic
60#107×C43—42no—
61#102×C43—42no—
62C24×C43—21no—
63C23×D43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C2×C22⋊D43—42no—
74C2×C22⋊D43—42no—
75C2×C22⋊D43—42no—
76C2×C22⋊D43—81no—
77C2×C22⋊D43—81no—
78C2×C22⋊D43—81no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C2×D172—21no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172D812yes—
86C2×C4×D43—42no—
87C2×C4×D43—42no—
88C2×C4×D43—81no—
89C2×C8×C43—22no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C22⋊Dic43—42no—
105C22⋊Dic43—81no—
106(C2×D43)⋊C4—42no—
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—41no—
111C4⋊Dic43—21no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C4⋊Dic43D812yes—
115Dic43⋊C4—42no—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43#12011yescharacteristic
132C22×D43—22no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139D4×C43—42no—
140D4×C43—81no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43#13511yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C22⋊D43—84no—
160C22⋊D43—84no—
161C2×Dic43—22no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170D172—42no—
171D172—81no—
172C4×D43—84no—
173C8×C43—42no—
174C43⋊C8—42no—
175C43⋊C8—81no—
176#7790—431nomaximal, Sylow
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43#44711yescharacteristic
185C22×C43#44711yescharacteristic
186C22×C43#45211yescharacteristic
187C22×C43#45311yescharacteristic
188C22×C43#45511yescharacteristic
189C22×C43#45611yescharacteristic
190C22×C43#45811yescharacteristic
191C2×D43—42no—
192C2×D43—42no—
193C2×D43—42no—
194C2×D43—81no—
195C2×D43—81no—
196C2×D43—81no—
197C2×D43—81no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—81no—
205C4×C43—161no—
206Dic43—42no—
207Dic43—81no—
208Dic43—81no—
209#2682—431no—
210#2093D4311yescharacteristic, complemented
211#2083—431no—
212#2071—431no—
213#1271—431no—
214#1270—431no—
215#1270—431no—
216C2×C43—161no—
217C2×C43#160711yescharacteristic
218C2×C43#161011yescharacteristic
219C2×C43#161811yescharacteristic
220C2×C43#161911yescharacteristic
221C2×C43#164111yescharacteristic
222C2×C43#164711yescharacteristic
223C2×C43#166111yescharacteristic
224D43—82no—
225C2×#123—861no—
226C2×#121—861no—
227C2×#107—21no—
228C2×#107—861no—
229C2×#102—21no—
230C2×#102—861no—
231#396—861no—
232#394—861no—
233#392—861no—
234#390—431no—
235#390C2×D4311yescharacteristic
236#389—431no—
237#385—861no—
238#384C2×D4311yescharacteristic
239#340—861no—
240#340—861no—
241#336—431no—
242#336—431no—
243#336C2×D4311yescharacteristic
244C43#779011yescharacteristic, complemented, Sylow
245C22×D4—431no—
246C22×D4—861no—
247C22×D4—861no—
248C22×D4C22⋊D4311yescharacteristic
249C23×C4—861no—
250C22×C8—21no—
251C22×C8—861no—
252C22×C8—861no—
253#123—1722no—
254#123—1722no—
255#121—1722no—
256#121—1722no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—431no—
261C2×C4⋊C4—431no—
262C2×C4⋊C4—431no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4C22⋊D4311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C42C22×D4311yescharacteristic
274#107—42no—
275#107—1722no—
276#102—42no—
277#102—1722no—
278#95—861no—
279#95—861no—
280C24—21no—
281C24—861no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—432no—
287C2×D4—861no—
288C2×D4—3441no—
289C2×D4—3441no—
290C2×D4—3441no—
291C2×D4—1721no—
292C2×D4—1721no—
293C2×D4—1722no—
294C2×D4—1722no—
295C2×D4—1722no—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4—861no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—3441no—
302C22×C4—1722no—
303C22×C4—1722no—
304C22×C4D4×D4311yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4C2×C22⋊D4311yescharacteristic
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—862no—
311C2×C8—1721no—
312C2×C8—1721no—
313C2×C8—1721no—
314C2×C8—1721no—
315C2×C8—1721no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—432no—
324C4⋊C4—861no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C4⋊C4—1722no—
328C4⋊C4—1721no—
329C4⋊C4—1721no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—3441no—
335C22⋊C4—1722no—
336C22⋊C4—1722no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C22⋊C4—1721no—
340C22⋊C4—1721no—
341C42—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—862no—
350C23—1721no—
351C23—1721no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23#1306329311yescharacteristic
357D4—42no—
358D4—81no—
359D4—3441no—
360D4—3444no—
361D4—3444no—
362D4—1722no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—862no—
376C2×C4—3444no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4D8×D4311yescharacteristic
386C2×C4D8×D4311yescharacteristic
387C2×C4#1306334511yescharacteristic
388C2×C4#1306334911yescharacteristic
389C2×C4#1306334911yescharacteristic
390C2×C4#1306335611yescharacteristic
391C8—42no—
392C8—3441no—
393C8—1722no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—3441no—
402C22—3441no—
403C22—3441no—
404C22—3441no—
405C22—1722no—
406C22—1722no—
407C22—1722no—
408C22#1458303111yescharacteristic
409C22#1458303111yescharacteristic
410C22#1458305911yescharacteristic
411C22#1458306611yescharacteristic
412C22#1458307511yescharacteristic
413C22#1458308011yescharacteristic
414C22#1458308811yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—161no—
423C4—3441no—
424C4—3441no—
425C4—1722no—
426C2—161no—
427C2—3442no—
428C2#1913357911yescharacteristic
429C2#1913359611yescharacteristic
430C2#1913364111yescharacteristic
431C2#1913364711yescharacteristic
432C2#1913378711yescharacteristic
433C2#1913382911yescharacteristic
434C2#1913390911yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2093C2
socleC23×C43#120
prime radical#19140958C2
hypercenter#2093D43
hypocenterC43#7790
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #19136067C2semidirect
3. #19135999C2semidirect
4. #19132417C2semidirect
5. #19132416C2semidirect
6. #19132415C2semidirect
7. C43×#2093C2semidirect
210. #2093D43semidirect
244. C43#7790semidirect

Maximal subgroups

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

subgroupindex
#191409582
#191360672
#191359992
#191324172
#191324162
#191324152
C43×#20932
#779043