Finite Group Databasebeta

← #25007612

Subgroups — #25007612

Order 11008.

776 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 776 conjugacy classes of subgroups — too many to draw. Only its 107 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#19134583C211yesmaximal, characteristic, complemented
2#19132916C211yesmaximal, characteristic, complemented
3#19132592C214yesmaximal, complemented
4C43×#2408C211yesmaximal, characteristic
5#14582952—21no—
6C2×#13063240—21no—
7#14582759—21no—
8#14582666C2212yescomplemented
9#14582623—21no—
10#14582623C2212yescomplemented
11C23×D4×C43C411yescharacteristic, complemented
12C2×#121×C43—21no—
13C2×#120×C43—21no—
14C2×C4×D4×C43C2211yescharacteristic
15C43×#394C412yescomplemented
16C43×#392C2212yes—
17C43×#390—21no—
18C43×#380C411yescharacteristic, complemented
19C43×#379—21no—
20C2×C4⋊Dic43—41no—
21C2×C22⋊Dic43—22no—
22C4⋊(C43⋊C8)—41no—
23#13063240—42no—
24C22⋊(C43⋊C8)—22no—
25C4×C43⋊C8—41no—
26C43⋊#95—41no—
27C25×C43—21no—
28C22×D4×C43—22no—
29C22×D4×C43—21no—
30C22×D4×C43—41no—
31C22×D4×C43—41no—
32C22×D4×C43—44no—
33C22×D4×C43C2×C412yes—
34C22×D4×C43D411yescharacteristic
35C23×C4×C43C2×C411yescharacteristic
36C23×C4×C43D411yescharacteristic
37#121×C43—44no—
38#120×C43—42no—
39#120×C43—42no—
40C4×D4×C43—41no—
41C4×D4×C43—41no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—22no—
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43—22no—
48C2×C22⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43C2311yescharacteristic
50C2×C42×C43D411yescharacteristic
51#95×C43C2×C412yes—
52C24×C43—22no—
53C24×C43—42no—
54C24×C43—44no—
55C24×C43—42no—
56C24×C43—42no—
57C24×C43—82no—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C2×D411yescharacteristic
60C2×D4×C43—24no—
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C2×D4×C43—44no—
64C2×D4×C43—44no—
65C2×D4×C43—42no—
66C2×D4×C43—44no—
67C2×D4×C43—48no—
68C2×D4×C43—44no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—42no—
72C2×D4×C43—42no—
73C2×D4×C43—42no—
74C2×D4×C43—82no—
75C2×D4×C43D812yes—
76C2×D4×C43SD1612yes—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—22no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22⋊C411yescharacteristic
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×Dic43—42no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—42no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—44no—
95C22⋊C4×C43—44no—
96C22⋊C4×C43—42no—
97C22⋊C4×C43—82no—
98C42×C43—21no—
99C42×C43—21no—
100C22⋊Dic43—42no—
101C22⋊Dic43—42no—
102C4⋊Dic43—82no—
103C2×C43⋊C8—42no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—24no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—42no—
116C23×C43—48no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—42no—
120C23×C43—84no—
121C23×C43—88no—
122C23×C43—88no—
123C23×C43—84no—
124C23×C43#10212yes—
125C23×C43C2×C22⋊C411yescharacteristic
126C23×C43C2×D811yescharacteristic
127C23×C43C2×SD1611yescharacteristic
128D4×C43—42no—
129D4×C43—42no—
130D4×C43—44no—
131D4×C43—44no—
132D4×C43—44no—
133D4×C43—44no—
134D4×C43—84no—
135D4×C43—84no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—22no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—81no—
152C2×C4×C43#9911yescharacteristic
153C2×C4×C43#9911yescharacteristic
154C2×C4×C43#10212yes—
155C2×Dic43—82no—
156C2×Dic43—82no—
157C2×Dic43—82no—
158C43⋊C8—82no—
159#11873—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—22no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—42no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—42no—
169C22×C43—44no—
170C22×C43—44no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—44no—
176C22×C43—81no—
177C22×C43—82no—
178C22×C43—82no—
179C22×C43—816no—
180C22×C43—82no—
181C22×C43—82no—
182C22×C43C2×#9911yescharacteristic
183C22×C43C2×#10211yescharacteristic
184C22×C43#42111yescharacteristic
185C4×C43—21no—
186C4×C43—22no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—41no—
190C4×C43—82no—
191C4×C43AΣL(1,𝔽16)12yes—
192Dic43—162no—
193#2408D4311yescharacteristic
194#1799—431no—
195#1460—431no—
196#1343—434no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—41no—
200C2×C43—42no—
201C2×C43—41no—
202C2×C43—84no—
203C2×C43#151911yescharacteristic
204C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
205C2×C43#212811yescharacteristic
206C23×D4Dic4311yescharacteristic, complemented
207C2×#121—21no—
208C2×#120—21no—
209C2×C4×D4C2×D4311yescharacteristic
210#431—861no—
211C2×#99—861no—
212#394Dic4312yescomplemented
213#392C2×D4312yes—
214#390—21no—
215#380—861no—
216#380Dic4311yescharacteristic, complemented
217#379—21no—
218#342—432no—
219#323—432no—
220#323—861no—
221C43#1187311yescharacteristic, complemented, Sylow
222C25—21no—
223C22×D4—22no—
224C22×D4—21no—
225C22×D4—41no—
226C22×D4—41no—
227C22×D4—44no—
228C22×D4C2×Dic4312yes—
229C22×D4C22⋊D4311yescharacteristic
230C23×C4C2×Dic4311yescharacteristic
231C23×C4C22⋊D4311yescharacteristic
232#121—44no—
233#120—42no—
234#120—42no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—1721no—
239C2×C4⋊C4C2×Dic4311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—862no—
245C2×C22⋊C4C22⋊D4311yescharacteristic
246C2×C22⋊C4C22×D4311yescharacteristic
247C2×C42C22⋊D4311yescharacteristic
248C4⋊C8—1721no—
249#99—1722no—
250C22⋊C8—862no—
251C4×C8—1721no—
252#95—1721no—
253#95C2×Dic4312yes—
254C24—22no—
255C24—42no—
256C24—44no—
257C24—42no—
258C24—42no—
259C24—82no—
260C24C22⋊Dic4311yescharacteristic
261C24C2×C22⋊D4311yescharacteristic
262C2×D4—24no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—48no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—82no—
277C2×D4#1062188212yes—
278C2×D4#1062188312yes—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—1722no—
287C22×C4C22⋊Dic4311yescharacteristic
288C22×C4C22⋊Dic4311yescharacteristic
289C22×C4C22⋊Dic4311yescharacteristic
290C22×C4C22×Dic4311yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292C2×C8—1722no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—3442no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—44no—
299C22⋊C4—42no—
300C22⋊C4—44no—
301C22⋊C4—82no—
302C22⋊C4—1722no—
303C22⋊C4—1722no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—24no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—48no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—84no—
323C23—88no—
324C23—88no—
325C23—84no—
326C23#1306324612yes—
327C23C2×C22⋊Dic4311yescharacteristic
328C23C2×#1062188211yescharacteristic
329C23C2×#1062188311yescharacteristic
330D4—42no—
331D4—42no—
332D4—44no—
333D4—44no—
334D4—44no—
335D4—44no—
336D4—84no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—3442no—
355C2×C4—3442no—
356C2×C4—3442no—
357C2×C4#1306324011yescharacteristic
358C2×C4#1306324011yescharacteristic
359C2×C4#1306324612yes—
360C8—3442no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—42no—
370C22—44no—
371C22—44no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—44no—
377C22—81no—
378C22—82no—
379C22—82no—
380C22—816no—
381C22—82no—
382C22—82no—
383C22C2×#1306324011yescharacteristic
384C22C2×#1306324611yescharacteristic
385C22#1458291611yescharacteristic
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—82no—
392C4—6882no—
393C4#1458268612yes—
394C2—21no—
395C2—21no—
396C2—41no—
397C2—42no—
398C2—41no—
399C2—84no—
400C2#1913316311yescharacteristic
401C2C2×#1458268611yescharacteristic
402C2#1913626711yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
Fitting, prime radicalC43×#2408C2
socleC22×C43C2×#99
cosocleC2×C22⋊C4×C43C23
hypercenter#2408D43
hypocenterC43#11873
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. #19134583C2semidirect
2. #19132916C2semidirect
3. #19132592C2semidirect
8. #14582666C22semidirect
10. #14582623C22semidirect
11. C23×D4×C43C4semidirect
15. C43×#394C4semidirect
18. C43×#380C4semidirect
206. C23×D4Dic43semidirect
212. #394Dic43semidirect
216. #380Dic43semidirect
221. C43#11873semidirect

Maximal subgroups

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

subgroupindex
#191345832
#191329162
#191325922
C43×#24082
#1187343