Finite Group Databasebeta

← #25069012

Subgroups — #25069012

Order 11008.

1054 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×#14583525C211yesmaximal, characteristic
2#19144543C212yesmaximal, complemented
3#19133619C214yesmaximal, complemented
4#19133585C214yesmaximal, complemented
5#19133127C212yesmaximal, complemented
6#19132922C211yesmaximal, characteristic
7C43×#2482C211yesmaximal, characteristic
8#14583525—24no—
9#14583525—22no—
10#14583525C2214yes—
11C2×#13063304—21no—
12C2×#13063304C2212yes—
13C2×#13063302—22no—
14C2×#13063302—22no—
15C22×C22⋊Dic43—21no—
16#14583240—24no—
17#14583234C2214yescomplemented
18#14583229C2214yescomplemented
19#14582942—22no—
20#14582907—22no—
21#14582863C2212yes—
22#14582635C2218yescomplemented
23#14582623C2214yes—
24C2×#117×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2211yescharacteristic
26C43×#399C2212yes—
27C43×#397C2212yes—
28C43×#388—22no—
29C43×#385—21no—
30C43×#381C2211yescharacteristic
31C43×#379—21no—
32C22×Dic86—21no—
33C22×Dic86D412yes—
34C23×Dic43—21no—
35C23×Dic43—21no—
36C2×#10621877—22no—
37#13063304—24no—
38#13063304—24no—
39#13063304—22no—
40#13063304—22no—
41#13063304D414yes—
42#13063304C2314yes—
43#13063302—28no—
44#13063302—28no—
45#13063302—28no—
46#13063302—28no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43D412yes—
49C2×Dic43⋊C4—22no—
50C2×Dic43⋊C4—22no—
51C2×C22⋊Dic43—22no—
52C2×C22⋊Dic43—24no—
53C2×C22⋊Dic43—22no—
54C2×C22⋊Dic43—24no—
55#13063258—24no—
56#13063256—24no—
57#13063248—24no—
58#13063248—24no—
59C22⋊(C43⋊C8)—22no—
60C22⋊(C43⋊C8)C2314yes—
61C25×C43D411yescharacteristic
62C23×C4×C43D411yescharacteristic
63C23×C4×C43C2311yescharacteristic
64#117×C43—22no—
65#117×C43—22no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43C2311yescharacteristic
68C2×C4⋊C4×C43C2311yescharacteristic
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43D412yes—
76C2×C22⋊C4×C43C2312yes—
77C2×C42×C43—21no—
78#95×C43—21no—
79#95×C43—22no—
80#95×C43C2312yes—
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—24no—
84C24×C43—42no—
85C24×C43—81no—
86C24×C43C2×D411yescharacteristic
87C24×C43C2×D412yes—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—22no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—42no—
94C22×C4×C43—81no—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2411yescharacteristic
100C22×Dic43—24no—
101C22×Dic43—24no—
102C22×Dic43—22no—
103C22×Dic43—22no—
104C22×Dic43—82no—
105C22×Dic43—82no—
106C2×Dic86—24no—
107C2×Dic86—22no—
108C2×Dic86—44no—
109C2×Dic86—82no—
110C2×Dic86C2×D414yes—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—82no—
114C22⋊C4×C43—24no—
115C22⋊C4×C43—24no—
116C22⋊C4×C43—42no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—44no—
120C22⋊C4×C43—82no—
121C42×C43—42no—
122C22⋊Dic43—28no—
123C22⋊Dic43—24no—
124C22⋊Dic43—24no—
125C4⋊Dic43—24no—
126C4⋊Dic43—22no—
127C4⋊Dic43C2×D414yes—
128Dic43⋊C4—28no—
129Dic43⋊C4—24no—
130Dic43⋊C4—24no—
131#10621877—44no—
132C2×C43⋊C8—24no—
133C23×C43—24no—
134C23×C43—24no—
135C23×C43—22no—
136C23×C43—22no—
137C23×C43—22no—
138C23×C43—22no—
139C23×C43—41no—
140C23×C43—42no—
141C23×C43—42no—
142C23×C43—42no—
143C23×C43—42no—
144C23×C43—81no—
145C23×C43—81no—
146C23×C43—88no—
147C23×C43#12011yescharacteristic
148C23×C43#12011yescharacteristic
149C23×C43#13714yes—
150C23×C43C22×D411yescharacteristic
151C2×C4×C43—24no—
152C2×C4×C43—22no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—81no—
166C2×C4×C43#12012yes—
167C2×C4×C43C22×D412yes—
168C2×Dic43—24no—
169C2×Dic43—24no—
170C2×Dic43—44no—
171C2×Dic43—44no—
172C2×Dic43—84no—
173C2×Dic43—84no—
174Dic86—44no—
175Dic86—82no—
176Dic86—84no—
177C43⋊C8—44no—
178#18138—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—24no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—44no—
188C22×C43—44no—
189C22×C43—48no—
190C22×C43—42no—
191C22×C43—42no—
192C22×C43—82no—
193C22×C43—84no—
194C22×C43#45812yes—
195C22×C43C2×#12011yescharacteristic
196C22×C43C2×#13712yes—
197C4×C43—22no—
198C4×C43—22no—
199C4×C43—42no—
200C4×C43—82no—
201C4×C43—81no—
202C4×C43—81no—
203Dic43—44no—
204Dic43—44no—
205C2×#543—431no—
206#3095—432no—
207#2482D4311yescharacteristic
208#1614—434no—
209#1608—434no—
210#1511—432no—
211#1462—431no—
212C2×C43—22no—
213C2×C43—22no—
214C2×C43—41no—
215C2×C43—44no—
216C2×C43#300411yescharacteristic
217C2×C43#301911yescharacteristic
218C2×C43C2×#45811yescharacteristic
219#543—434no—
220#543—864no—
221#543—862no—
222C2×C22⋊Q8—432no—
223C2×C22⋊Q8—862no—
224C2×C22⋊Q8—862no—
225C2×C22⋊Q8—861no—
226C2×#117C2×D4311yescharacteristic
227C22×C22⋊C4—861no—
228C22×C22⋊C4C2×D4311yescharacteristic
229#485—864no—
230#484—434no—
231#483—434no—
232#428—862no—
233#419—862no—
234#407—432no—
235#399C2×D4312yes—
236#397C2×D4312yes—
237#388—22no—
238#385—21no—
239#381C2×D4311yescharacteristic
240#379—21no—
241#328—438no—
242#323—434no—
243C43#1813811yescharacteristic, complemented, Sylow
244C25C22⋊D4311yescharacteristic
245C22×Q8—432no—
246C22×Q8—861no—
247C23×C4—861no—
248C23×C4—861no—
249C23×C4C22⋊D4311yescharacteristic
250C23×C4C22×D4311yescharacteristic
251C2×M16—862no—
252C22⋊Q8—434no—
253C22⋊Q8—434no—
254C22⋊Q8—868no—
255C22⋊Q8—868no—
256C22⋊Q8—868no—
257C22⋊Q8—868no—
258C22⋊Q8—864no—
259C22⋊Q8—862no—
260C22⋊Q8—862no—
261C22⋊Q8—864no—
262#117—22no—
263#117—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—432no—
266C2×C4⋊C4—862no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—862no—
269C2×C4⋊C4C22×D4311yescharacteristic
270C2×C4⋊C4C22×D4311yescharacteristic
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—864no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—864no—
281C2×C22⋊C4C22⋊D4312yes—
282C2×C22⋊C4C22×D4312yes—
283C2×C42—21no—
284#107—864no—
285#106—864no—
286#103—864no—
287#103—864no—
288C22⋊C8—434no—
289C22⋊C8—862no—
290#95—21no—
291#95—22no—
292#95C22×D4312yes—
293C24—21no—
294C24—21no—
295C24—24no—
296C24—42no—
297C24—81no—
298C24C2×C22⋊D4311yescharacteristic
299C24C2×C22⋊D4312yes—
300C2×Q8—434no—
301C2×Q8—864no—
302C2×Q8—862no—
303C2×Q8—3442no—
304C2×Q8—1724no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—81no—
312C22×C4—864no—
313C22×C4—864no—
314C22×C4—862no—
315C22×C4—862no—
316C22×C4—3442no—
317C22×C4—3442no—
318C22×C4D4×D4312yes—
319C22×C4D4×D4312yes—
320C22×C4C2×C22⋊D4312yes—
321C22×C4C2×C22⋊D4311yescharacteristic
322C22×C4C23×D4311yescharacteristic
323M16—1724no—
324C2×C8—864no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—82no—
328C4⋊C4—434no—
329C4⋊C4—868no—
330C4⋊C4—864no—
331C4⋊C4—862no—
332C4⋊C4—864no—
333C4⋊C4—864no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—44no—
340C22⋊C4—82no—
341C22⋊C4—868no—
342C22⋊C4—864no—
343C22⋊C4—864no—
344C42—42no—
345C23—24no—
346C23—24no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—81no—
357C23—81no—
358C23—88no—
359C23#1306329311yescharacteristic
360C23#1306329311yescharacteristic
361C23#1306335514yes—
362C23C22×C22⋊D4311yescharacteristic
363Q8—3442no—
364Q8—3444no—
365Q8—1724no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—864no—
382C2×C4—864no—
383C2×C4—3444no—
384C2×C4—3444no—
385C2×C4—1724no—
386C2×C4—1724no—
387C2×C4#1306329312yes—
388C2×C4C2×D4×D4312yes—
389C8—1724no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—24no—
398C22—44no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—84no—
405C22#1458308812yes—
406C22C2×#1306329311yescharacteristic
407C22C2×#1306335512yes—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—82no—
412C4—81no—
413C4—81no—
414C4—1724no—
415C4—1724no—
416C2—22no—
417C2—22no—
418C2—41no—
419C2—44no—
420C2#1914382811yescharacteristic
421C2#1914395111yescharacteristic
422C2C2×#1458308811yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2482C2
socleC22×C43C2×#120
prime radicalC25×C43D4
hypercenter#2482D43
hypocenterC43#18138
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
2. #19144543C2semidirect
3. #19133619C2semidirect
4. #19133585C2semidirect
5. #19133127C2semidirect
17. #14583234C22semidirect
18. #14583229C22semidirect
22. #14582635C22semidirect
243. C43#18138semidirect

Maximal subgroups

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

subgroupindex
C2×#145835252
#191445432
#191336192
#191335852
#191331272
#191329222
C43×#24822
#1813843