Finite Group Databasebeta

← #24985474

Subgroups — #24985474

Order 11008.

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

normal subgroups only

This group has 446 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#19135923C211yesmaximal, characteristic, complemented
2#19135841C211yesmaximal, characteristic, complemented
3#19135731C211yesmaximal, characteristic
4#19132418C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132416C211yesmaximal, characteristic
7C43×#2727C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063258—21no—
10C2×#13063248—21no—
11C2×#13063248—21no—
12C2×#13063246—21no—
13#14582661—21no—
14#14582661—21no—
15#14582654C2211yescharacteristic
16#14582654C2211yescharacteristic
17#14582654C2211yescharacteristic
18C2×#126×C43—21no—
19C43×#399—21no—
20C43×#396—21no—
21C43×#394—21no—
22C43×#390C2211yescharacteristic
23C43×#389—21no—
24C43×#389C2211yescharacteristic
25C43×#389C2211yescharacteristic
26C43×#388—21no—
27C22×Dic86—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063325—42no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34#13063258—42no—
35#13063248—42no—
36#13063248—42no—
37#13063246—42no—
38C22×D4×C43D411yescharacteristic
39#126×C43—42no—
40#126×C43—42no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C42×C43—21no—
57C2×C42×C43C2311yescharacteristic
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61C24×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—41no—
65C2×D4×C43—41no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—41no—
75C2×Dic86—22no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—42no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—81no—
93C4⋊C4×C43D812yes—
94C22⋊C4×C43—42no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—81no—
101C22⋊C4×C43—81no—
102C42×C43—41no—
103C42×C43—42no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43#12011yescharacteristic
125D4×C43—42no—
126D4×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—22no—
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×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43C2×D811yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43#13711yescharacteristic
153C2×C4×C43#13711yescharacteristic
154C2×Dic43—42no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157Dic86—42no—
158Dic86—42no—
159Dic86—81no—
160Dic86—81no—
161C43⋊C8—42no—
162C43⋊C8—81no—
163C43⋊C8—81no—
164#7765—431nomaximal, Sylow
165C22×C43—81no—
166C22×C43—81no—
167C22×C43—81no—
168C22×C43—81no—
169C22×C43—81no—
170C22×C43—81no—
171C22×C43—81no—
172C22×C43#44711yescharacteristic
173C22×C43#45211yescharacteristic
174C22×C43#45211yescharacteristic
175C22×C43#45411yescharacteristic
176C22×C43#45511yescharacteristic
177C22×C43#45611yescharacteristic
178C22×C43B(4,𝔽2)11yescharacteristic
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—42no—
186C4×C43—81no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43—81no—
190Dic43—82no—
191#2727D4311yescharacteristic
192#2057—431no—
193#2043—431no—
194#2023—431no—
195#1271—431no—
196#1271—431no—
197#1270—431no—
198C2×C43—161no—
199C2×C43#159811yescharacteristic
200C2×C43#160311yescharacteristic
201C2×C43#160611yescharacteristic
202C2×C43#163811yescharacteristic
203C2×C43#164111yescharacteristic
204C2×C43#164711yescharacteristic
205C2×C43#166411yescharacteristic
206C2×C4⋊Q8—431no—
207C2×#126—21no—
208C2×#107—861no—
209C2×#103—861no—
210C2×#103—861no—
211C2×#102—861no—
212#399—21no—
213#396—21no—
214#394—21no—
215#390C2×D4311yescharacteristic
216#389—21no—
217#389C2×D4311yescharacteristic
218#389C2×D4311yescharacteristic
219#388—21no—
220#340—861no—
221#340—861no—
222#336—431no—
223#336—431no—
224#336—431no—
225C43#776511yescharacteristic, complemented, Sylow
226C22×Q8—861no—
227C22×D4C22⋊D4311yescharacteristic
228C22×C8—861no—
229C22×C8—861no—
230C22×C8—861no—
231C4⋊Q8—1722no—
232#126—42no—
233#126—42no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4C22⋊D4311yescharacteristic
241C2×C4⋊C4C22⋊D4311yescharacteristic
242C2×C4⋊C4C22⋊D4311yescharacteristic
243C2×C4⋊C4C22⋊D4311yescharacteristic
244C2×C4⋊C4C22⋊D4311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C42—21no—
252C2×C42C22×D4311yescharacteristic
253#107—1722no—
254#103—1722no—
255#103—1722no—
256#102—1722no—
257#95—21no—
258#95—21no—
259#95—21no—
260C24—21no—
261C2×Q8—862no—
262C2×Q8—1721no—
263C2×Q8—1721no—
264C2×Q8—1721no—
265C2×Q8—1721no—
266C2×Q8—1721no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—1721no—
277C22×C4C2×C22⋊D4311yescharacteristic
278C22×C4C2×C22⋊D4311yescharacteristic
279C22×C4C2×C22⋊D4311yescharacteristic
280C2×C8—862no—
281C2×C8—1721no—
282C2×C8—1721no—
283C2×C8—1721no—
284C2×C8—1721no—
285C2×C8—1721no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8—1721no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4—862no—
302C4⋊C4—862no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4#1062188212yes—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—81no—
313C22⋊C4—81no—
314C42—41no—
315C42—42no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23#1306329411yescharacteristic
324Q8—3441no—
325Q8—3441no—
326Q8—1722no—
327Q8—1722no—
328D4—42no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—1722no—
354C2×C4C2×#1062188211yescharacteristic
355C2×C4#1306334511yescharacteristic
356C2×C4#1306334511yescharacteristic
357C2×C4#1306335111yescharacteristic
358C2×C4#1306335511yescharacteristic
359C2×C4#1306335511yescharacteristic
360C8—3441no—
361C8—3441no—
362C8—1722no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22#1458303311yescharacteristic
371C22#1458306111yescharacteristic
372C22#1458306111yescharacteristic
373C22#1458307211yescharacteristic
374C22#1458307711yescharacteristic
375C22#1458308211yescharacteristic
376C22#1458308611yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—42no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—3442no—
389C2—161no—
390C2#1913353011yescharacteristic
391C2#1913355811yescharacteristic
392C2#1913357511yescharacteristic
393C2#1913376711yescharacteristic
394C2#1913378811yescharacteristic
395C2#1913383011yescharacteristic
396C2#1913392911yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2727C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#2727D43
hypocenterC43#7765
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2727

Complements

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

NH ≅ G/Ntype
1. #19135923C2semidirect
2. #19135841C2semidirect
4. #19132418C2semidirect
5. #19132418C2semidirect
225. C43#7765semidirect

Maximal subgroups

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

subgroupindex
#191359232
#191358412
#191357312
#191324182
#191324162
C43×#27272
#776543