Finite Group Databasebeta

← #24993528

Subgroups — #24993528

Order 11008.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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#19144726C211yesmaximal, characteristic
2#19137247C211yesmaximal, characteristic
3#19135539C211yesmaximal, characteristic
4#19133106C211yesmaximal, characteristic
5#19133043C211yesmaximal, characteristic
6#19132452C211yesmaximal, characteristic
7C43×#1300C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583230—21no—
11#14583185C412yescomplemented
12#14583110C412yescomplemented
13#14583057—21no—
14#14583007—22no—
15#14582956C2211yescharacteristic
16#14582805—21no—
17#14582797—21no—
18#14582781—22no—
19#14582766—21no—
20#14582763—21no—
21C4×C4⋊Dic43C2211yescharacteristic
22#14582660—22no—
23#14582635—21no—
24#14582635—21no—
25#14582631—22no—
26C43×#432C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C43×#376C2211yescharacteristic
29C22×Dic86D411yescharacteristic
30C2×Dic172—22no—
31#13063325C2×C411yescharacteristic
32#13063325C2×C411yescharacteristic
33#13063317—21no—
34#13063304—21no—
35#13063304—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86C2×C412yes—
41C4×Dic86D412yes—
42#13063284—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—22no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43D412yes—
49#13063257—22no—
50C4⋊(C43⋊C8)—21no—
51#13063250—22no—
52#13063250—22no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—22no—
58C43⋊#95—21no—
59C2×M16×C43—21no—
60C2×C42×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43C2×C412yes—
63C22⋊C8×C43—21no—
64#97×C43—21no—
65#97×C43—21no—
66C4×C8×C43—21no—
67#95×C43—21no—
68#95×C43D411yescharacteristic
69#95×C43D411yescharacteristic
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—22no—
78C2×Dic86—21no—
79C2×Dic86—21no—
80C2×Dic86—21no—
81C2×Dic86—42no—
82C2×Dic86C22⋊C412yes—
83M16×C43—22no—
84M16×C43—41no—
85C2×C8×C43—22no—
86C2×C8×C43—41no—
87C42×C43—42no—
88C42×C43C22×C411yescharacteristic
89C42×C43C2×D411yescharacteristic
90C42×C43#4111yescharacteristic
91C42×C43#4111yescharacteristic
92C22⋊Dic43—41no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—42no—
99C4⋊Dic43C22⋊C412yes—
100Dic43⋊C4—22no—
101Dic43⋊C4—22no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104Dic43⋊C4—82no—
105C4×Dic43—22no—
106C4×Dic43—22no—
107C4×Dic43—41no—
108C4×Dic43—42no—
109C2×C43⋊C8—41no—
110Dic172—44no—
111C23×C43#12011yescharacteristic
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—22no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43C2×C22⋊C411yescharacteristic
123C2×C4×C43C4×D411yescharacteristic
124C2×C4×C43C4×D411yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12311yescharacteristic
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—42no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—42no—
138Dic86—22no—
139Dic86—22no—
140Dic86—42no—
141Dic86—42no—
142Dic86—81no—
143C8×C43—42no—
144C8×C43—42no—
145C43⋊C8—81no—
146#9328—431nomaximal, Sylow
147C22×C43—21no—
148C22×C43—21no—
149C22×C43#38611yescharacteristic
150C22×C43#45511yescharacteristic
151C22×C43#45611yescharacteristic
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—81no—
158C4×C43—81no—
159C4×C43#42112yes—
160Dic43—42no—
161Dic43—42no—
162Dic43—82no—
163Dic43—81no—
164Dic43—81no—
165#3113—431no—
166#2320—431no—
167#1986—431no—
168#1506—431no—
169#1491—431no—
170#1300D4311yescharacteristic
171#1285—431no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43#188211yescharacteristic
175C2×C43#189711yescharacteristic
176C2×C43#190511yescharacteristic
177#533—431no—
178C2×C4×Q8—431no—
179#483—861no—
180#475—432no—
181#462—432no—
182#451—861no—
183#441—862no—
184#432—431no—
185#432C2×D4311yescharacteristic
186C4×M16C2×D4311yescharacteristic
187#391—861no—
188#389—861no—
189#387—862no—
190#383—861no—
191#382—861no—
192C4×C4⋊C4—431no—
193#376C2×D4311yescharacteristic
194#339—862no—
195#328—861no—
196#328—861no—
197Q8⋊C8—862no—
198C43#932811yescharacteristic, complemented, Sylow
199C22×Q8—431no—
200C2×Q16—862no—
201C2×M16—21no—
202C4⋊Q8—431no—
203C4⋊Q8—431no—
204#125—861no—
205C22⋊Q8—861no—
206C22⋊Q8—861no—
207C4×Q8—432no—
208C4×Q8—432no—
209C4×Q8—861no—
210C4×Q8—861no—
211C4×Q8—861no—
212C4×Q8—861no—
213#117—861no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—862no—
217C2×C4⋊C4—861no—
218C2×C42—21no—
219C2×C42—432no—
220C2×C42—861no—
221C2×C42C22×D4311yescharacteristic
222#106—862no—
223C4⋊C8—861no—
224C4⋊C8C4×D4312yes—
225#103—862no—
226#103—862no—
227C22⋊C8—21no—
228C22⋊C8—861no—
229#97—21no—
230#97—21no—
231#97—861no—
232C4×C8—21no—
233#95—21no—
234#95—862no—
235#95—862no—
236#95—862no—
237#95—861no—
238#95D17211yescharacteristic
239#95D17211yescharacteristic
240C2×Q8—432no—
241C2×Q8—861no—
242C2×Q8—861no—
243C2×Q8—861no—
244C2×Q8—1722no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—862no—
250C22×C4C2×D17211yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253Q16—1724no—
254M16—22no—
255M16—41no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—1721no—
259C4⋊C4—432no—
260C4⋊C4—862no—
261C4⋊C4—862no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—3442no—
268C4⋊C4—1722no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C22⋊C4—1721no—
272C42—42no—
273C42—862no—
274C42—862no—
275C42—1722no—
276C42—1721no—
277C42C2×C4×D4311yescharacteristic
278C42#1062189811yescharacteristic
279C42D4×D4311yescharacteristic
280C42#1062190211yescharacteristic
281C23#1306329511yescharacteristic
282Q8—862no—
283Q8—862no—
284Q8—3441no—
285Q8—1722no—
286Q8—1722no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—1722no—
300C2×C4—1722no—
301C2×C4—1722no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1722no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4C22⋊C4×D4311yescharacteristic
308C2×C4#1306328711yescharacteristic
309C2×C4C4×D17211yescharacteristic
310C2×C4#1306329811yescharacteristic
311C2×C4#1306330011yescharacteristic
312C2×C4#1306331011yescharacteristic
313C8—42no—
314C8—42no—
315C8—3441no—
316C22—21no—
317C22—21no—
318C22#1458277711yescharacteristic
319C22#1458307811yescharacteristic
320C22#1458308311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—3442no—
329C4—3441no—
330C4—3441no—
331C4—1722no—
332C4—1722no—
333C4#1458291412yes—
334C2—21no—
335C2—21no—
336C2#1913496511yescharacteristic
337C2#1913504211yescharacteristic
338C2#1913508811yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1300C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1300D43
hypocenterC43#9328
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
11. #14583185C4semidirect
12. #14583110C4semidirect
198. C43#9328semidirect

Maximal subgroups

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

subgroupindex
#191447262
#191372472
#191355392
#191331062
#191330432
#191324522
C43×#13002
#932843