Finite Group Databasebeta

← #25009432

Subgroups — #25009432

Order 11008.

394 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 59 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#19142296C211yesmaximal, characteristic
2#19133637C211yesmaximal, characteristic, complemented
3#19133569C211yesmaximal, characteristic, complemented
4#19132624C211yesmaximal, characteristic, complemented
5#19132621C211yesmaximal, characteristic, complemented
6#19132527C211yesmaximal, characteristic
7C43×#2027C211yesmaximal, characteristic
8#14583232—21no—
9#14583054—21no—
10#14582838C2211yescharacteristic
11#14582822—21no—
12#14582819C2211yescharacteristic
13#14582811—21no—
14#14582783—21no—
15#14582779—21no—
16#14582771—21no—
17#14582757—21no—
18#14582636—21no—
19#14582636—21no—
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#418—21no—
24C43×#390C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#339—21no—
27C22×Dic86D411yescharacteristic
28C23×Dic43—21no—
29C2×#10621885—41no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37#13063258—41no—
38#13063249—41no—
39#13063248—41no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C22×D4×C43D411yescharacteristic
50C2×M16×C43—21no—
51C4⋊Q8×C43—41no—
52#125×C43—41no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#117×C43—21no—
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43D411yescharacteristic
60#102×C43—41no—
61#102×C43—41no—
62C24×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43Q1612yescomplemented
69C22×C4×C43—21no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—42no—
78C22×Dic43—81no—
79C22×Dic43—81no—
80C2×Dic86—41no—
81C2×Dic86—81no—
82M16×C43—41no—
83M16×C43—41no—
84C2×C8×C43—41no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—81no—
94C22⋊C4×C43—81no—
95C42×C43—41no—
96C42×C43—41no—
97C22⋊Dic43—42no—
98C22⋊Dic43—81no—
99C22⋊Dic43—81no—
100#10621885—82no—
101C4⋊Dic43—41no—
102Dic43⋊C4—42no—
103Dic43⋊C4—81no—
104Dic43⋊C4—81no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43—22no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43#12011yescharacteristic
115Q8×C43—81no—
116Q8×C43—81no—
117D4×C43—42no—
118D4×C43—81no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43C2×Q1611yescharacteristic
131C2×C4×C43#13711yescharacteristic
132C2×Dic43—22no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—84no—
145Dic86—42no—
146Dic86—81no—
147C8×C43—81no—
148C43⋊C8—81no—
149C43⋊C8—81no—
150#12223—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43—42no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43—81no—
159C22×C43—81no—
160C22×C43#45111yescharacteristic
161C22×C43#45511yescharacteristic
162C22×C43B(4,𝔽2)11yescharacteristic
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—81no—
168C4×C43—81no—
169C4×C43—81no—
170Dic43—42no—
171Dic43—81no—
172Dic43—81no—
173Dic43—81no—
174#2784—431no—
175#2027D4311yescharacteristic
176#1617—431no—
177#1605—431no—
178#1354—431no—
179#1353—431no—
180#1318—431no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—82no—
184C2×C43#160211yescharacteristic
185C2×C43#220011yescharacteristic
186C2×C43#220411yescharacteristic
187#544C2×D4311yescharacteristic
188#484—861no—
189#451—861no—
190#418—21no—
191#400—431no—
192#396—861no—
193#395—431no—
194#393—861no—
195#390C2×D4311yescharacteristic
196#387—861no—
197#386—861no—
198#385—861no—
199#380—861no—
200#343C2×D4311yescharacteristic
201#339—21no—
202#328—861no—
203#328—861no—
204#324—431no—
205#324—431no—
206C43#1222311yescharacteristic, complemented, Sylow
207C22×Q8—431no—
208C22×D4C22⋊D4311yescharacteristic
209C23×C4—861no—
210C2×Q16—1721no—
211C2×M16—21no—
212C4⋊Q8—41no—
213#125—41no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216#117—21no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C22×D4311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—861no—
225C2×C22⋊C4—861no—
226C2×C22⋊C4—861no—
227C2×C42C22⋊D4311yescharacteristic
228#107—1721no—
229#103—1721no—
230#103—1721no—
231#102—41no—
232#102—41no—
233C22⋊C8—861no—
234C22⋊C8—861no—
235#95—431no—
236#95—431no—
237#95—861no—
238#95—861no—
239#95—861no—
240#95—861no—
241#95—861no—
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—3441no—
246C2×Q8—1721no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4#1062188512yescomplemented
251C22×C4—21no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—3441no—
257C22×C4—3441no—
258C22×C4—1722no—
259C22×C4D4×D4311yescharacteristic
260C22×C4D4×D4311yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262Q16—3442no—
263M16—41no—
264M16—41no—
265C2×C8—41no—
266C2×C8—1721no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—3441no—
276C4⋊C4—3441no—
277C4⋊C4—1721no—
278C4⋊C4—1722no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C22⋊C4—3441no—
283C22⋊C4—3441no—
284C22⋊C4—1722no—
285C42—41no—
286C42—41no—
287C23—22no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#1306329311yescharacteristic
295Q8—81no—
296Q8—81no—
297Q8—3441no—
298Q8—1722no—
299D4—42no—
300D4—81no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—862no—
313C2×C4—3444no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4C2×#1062188511yescharacteristic
326C2×C4#1306335511yescharacteristic
327C8—81no—
328C8—3441no—
329C8—3441no—
330C22—21no—
331C22—21no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22#1458305411yescharacteristic
340C22#1458307611yescharacteristic
341C22#1458308511yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—3441no—
350C4—3441no—
351C4—3441no—
352C4—1722no—
353C2—21no—
354C2—21no—
355C2—82no—
356C2#1913355111yescharacteristic
357C2#1913660111yescharacteristic
358C2#1913661911yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2027C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#2027D43
hypocenterC43#12223
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2027

Complements

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

NH ≅ G/Ntype
2. #19133637C2semidirect
3. #19133569C2semidirect
4. #19132624C2semidirect
5. #19132621C2semidirect
68. C2×D4×C43Q16semidirect
206. C43#12223semidirect
250. C2×D4#10621885semidirect

Maximal subgroups

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

subgroupindex
#191422962
#191336372
#191335692
#191326242
#191326212
#191325272
C43×#20272
#1222343