Finite Group Databasebeta

← #24985529

Subgroups — #24985529

Order 11008.

422 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 79 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#19142577C211yesmaximal, characteristic
2#19135838C211yesmaximal, characteristic, complemented
3#19135728C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic, complemented
5#19132417C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2024C211yesmaximal, characteristic, complemented
8C2×#13063249—21no—
9C2×#13063249—21no—
10C2×#13063245—21no—
11#14582826—21no—
12#14582817—21no—
13#14582810—21no—
14#14582801C2211yescharacteristic
15#14582797C2211yescharacteristic
16#14582791—21no—
17#14582789—21no—
18#14582786—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×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×C4×Dic43—21no—
41#13063249—42no—
42#13063249—42no—
43#13063245—42no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C22×Q8×C43—21no—
49C22×Q8×C43D411yescharacteristic
50C22×C8×C43—21no—
51C4⋊Q8×C43—42no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C42×C43C2311yescharacteristic
56#103×C43—42no—
57#95×C43—21no—
58#95×C43—21no—
59C23×D43—21no—
60C2×Q8×C43—22no—
61C2×Q8×C43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—41no—
82C2×D172—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C42×C43—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—81no—
97(C2×D43)⋊C4—81no—
98(C2×D43)⋊C4—81no—
99(C2×D43)⋊C4—81no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106C4×Dic43—81no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C23×C43#12011yescharacteristic
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121Q8×C43—42no—
122Q8×C43—42no—
123Q8×C43—42no—
124Q8×C43—81no—
125Q8×C43—81no—
126Q8×C43—81no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43#13511yescharacteristic
144C2×C4×C43#13511yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C2×C4×C43#13711yescharacteristic
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157D172—42no—
158D172—81no—
159C8×C43—81no—
160C43⋊C8—81no—
161C43⋊C8—81no—
162#7773—431nomaximal, Sylow
163C22×C43#44911yescharacteristic
164C22×C43#45211yescharacteristic
165C22×C43#45211yescharacteristic
166C22×C43#45411yescharacteristic
167C22×C43#45511yescharacteristic
168C22×C43#45511yescharacteristic
169C22×C43B(4,𝔽2)11yescharacteristic
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—82no—
184C4×C43—81no—
185C4×C43—81no—
186Dic43—81no—
187Dic43—81no—
188Dic43—81no—
189#2808—431no—
190#2043—431no—
191#2024D4311yescharacteristic, complemented
192#2023—431no—
193#1272—431no—
194#1271—431no—
195#1270—431no—
196C2×C43#159711yescharacteristic
197C2×C43#160611yescharacteristic
198C2×C43#160611yescharacteristic
199C2×C43#163811yescharacteristic
200C2×C43#164011yescharacteristic
201C2×C43#164611yescharacteristic
202C2×C43#166211yescharacteristic
203D43—161no—
204C2×C4⋊Q8C2×D4311yescharacteristic
205C2×#103—21no—
206C2×#103—861no—
207C2×#103—861no—
208C2×#102—861no—
209#397—861no—
210#394—861no—
211#393—861no—
212#391C2×D4311yescharacteristic
213#390—431no—
214#389—431no—
215#388—861no—
216#388—861no—
217#387—861no—
218#340—21no—
219#340—861no—
220#336—431no—
221#336—431no—
222#336C2×D4311yescharacteristic
223C43#777311yescharacteristic, complemented, Sylow
224C22×Q8—21no—
225C22×Q8C22⋊D4311yescharacteristic
226C22×D4—431no—
227C22×C8—21no—
228C22×C8—861no—
229C22×C8—861no—
230C4⋊Q8—42no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4C22⋊D4311yescharacteristic
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C42—861no—
245C2×C42C22×D4311yescharacteristic
246#103—42no—
247#103—1722no—
248#103—1722no—
249#102—1722no—
250#95—21no—
251#95—21no—
252#95—861no—
253#95—861no—
254#95—861no—
255#95—861no—
256C24—861no—
257C2×Q8—22no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—1721no—
270C2×D4—1721no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4D4×D4311yescharacteristic
278C22×C4D4×D4311yescharacteristic
279C22×C4C2×C22⋊D4311yescharacteristic
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—1721no—
284C2×C8—1721no—
285C2×C8—1721no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8—1721no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C22⋊C4—3441no—
301C22⋊C4—3441no—
302C22⋊C4—3441no—
303C22⋊C4—3441no—
304C22⋊C4—1721no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C22⋊C4—1721no—
308C42—41no—
309C42—3441no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23—1721no—
314C23—1721no—
315C23—1721no—
316C23—1721no—
317C23#1306329311yescharacteristic
318Q8—42no—
319Q8—42no—
320Q8—42no—
321Q8—81no—
322Q8—81no—
323Q8—81no—
324D4—3441no—
325D4—1722no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4#1306334511yescharacteristic
351C2×C4#1306334611yescharacteristic
352C2×C4#1306334811yescharacteristic
353C2×C4#1306335211yescharacteristic
354C2×C4#1306335611yescharacteristic
355C2×C4#1306335711yescharacteristic
356C8—81no—
357C8—3441no—
358C8—3441no—
359C22—3441no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22—3441no—
366C22#1458304311yescharacteristic
367C22#1458305911yescharacteristic
368C22#1458306011yescharacteristic
369C22#1458307011yescharacteristic
370C22#1458307511yescharacteristic
371C22#1458307611yescharacteristic
372C22#1458308511yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—81no—
381C4—81no—
382C4—3441no—
383C4—3441no—
384C4—3441no—
385C2—6881no—
386C2#1913352311yescharacteristic
387C2#1913357311yescharacteristic
388C2#1913357411yescharacteristic
389C2#1913376611yescharacteristic
390C2#1913378011yescharacteristic
391C2#1913382011yescharacteristic
392C2#1913391711yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2024C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2024D43
hypocenterC43#7773
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. #19132417C2semidirect
7. C43×#2024C2semidirect
191. #2024D43semidirect
223. C43#7773semidirect

Maximal subgroups

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

subgroupindex
#191425772
#191358382
#191357282
#191324212
#191324172
#191324152
C43×#20242
#777343