Finite Group Databasebeta

← #25006059

Subgroups — #25006059

Order 11008.

442 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 75 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#19137263C211yesmaximal, characteristic
2#19132934C211yesmaximal, characteristic
3#19132930C211yesmaximal, characteristic
4#19132543C211yesmaximal, characteristic, complemented
5#19132524C211yesmaximal, characteristic, complemented
6#19132524C211yesmaximal, characteristic, complemented
7C43×#1326C211yesmaximal, characteristic, complemented
8C2×#13063309C411yescharacteristic
9C2×(C22⋊D43)⋊C4C2211yescharacteristic
10C22×Dic43⋊C4C411yescharacteristic
11#14582953—21no—
12#14582861—21no—
13#14582795—21no—
14#14582788—21no—
15#14582782—21no—
16#14582778C411yescharacteristic
17#14582770—21no—
18#14582760C2211yescharacteristic
19C22⋊C4×Dic43C411yescharacteristic
20#14582624—21no—
21#14582623C2211yescharacteristic
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#385C2211yescharacteristic
25C43×#323C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621872—41no—
32#13063309—22no—
33#13063309—22no—
34(C22⋊D43)⋊C4—41no—
35(C22⋊D43)⋊C4—41no—
36C2×C4⋊Dic43—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—41no—
40C2×Dic43⋊C4—41no—
41C2×Dic43⋊C4D411yescharacteristic
42C2×C22⋊Dic43C2×C411yescharacteristic
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43D411yescharacteristic
48Dic43⋊C8—41no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51(C2×D43)⋊C8—41no—
52#13063235—41no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C23×C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43—21no—
59C2×C22⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62C22⋊C8×C43—21no—
63#95×C43—21no—
64C24×C43C22×C411yescharacteristic
65C23×D43C22⋊C411yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—41no—
69C22×C4×C43—81no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—41no—
82C22×Dic43—41no—
83C22×Dic43—81no—
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43M1612yescomplemented
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—81no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C4⋊C4×C43—81no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43M1612yescomplemented
97C22⋊Dic43—41no—
98(C2×D43)⋊C4—24no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—81no—
101C4⋊Dic43—24no—
102Dic43⋊C4—41no—
103Dic43⋊C4—42no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43—81no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111#10621872—82no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43C2×C22⋊C411yescharacteristic
117C23×C43C2×M1611yescharacteristic
118C23×C43C2×M1611yescharacteristic
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—41no—
123C22×D43—41no—
124C2×C4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—82no—
135C22⋊D43—42no—
136C22⋊D43—42no—
137C2×Dic43—21no—
138C2×Dic43—22no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—42no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43#9911yescharacteristic
154C2×Dic43#9911yescharacteristic
155C4×D43—42no—
156C4×D43—81no—
157C8×C43—81no—
158C8×C43—81no—
159C43⋊C8—81no—
160C43⋊C8—81no—
161#11528—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—42no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43#40711yescharacteristic
172C22×C43C2×#9911yescharacteristic
173C22×C43#41311yescharacteristic
174C2×D43—42no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—81no—
179C4×C43—42no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—81no—
183Dic43—21no—
184Dic43—21no—
185Dic43—41no—
186Dic43—41no—
187Dic43—42no—
188Dic43—81no—
189#2322—431no—
190#1466—431no—
191#1465—431no—
192#1326—431no—
193#1326D4311yescharacteristic, complemented
194#1317—431no—
195#1317—431no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43—41no—
199C2×C43—41no—
200C2×C43#146511yescharacteristic
201C2×C43#212111yescharacteristic
202C2×C43#212311yescharacteristic
203D43—81no—
204C2×#123—431no—
205C2×C4×D4—431no—
206C22×C4⋊C4—431no—
207#432—861no—
208#407—861no—
209#389—861no—
210#388—861no—
211#387—861no—
212#386—431no—
213#385—861no—
214#385C2×D4311yescharacteristic
215#381—431no—
216C4×C22⋊C4—431no—
217#324—861no—
218#323—431no—
219#323—431no—
220#323—861no—
221#323C2×D4311yescharacteristic
222#323C2×D4311yescharacteristic
223C43#1152811yescharacteristic, complemented, Sylow
224C22×D4—431no—
225C23×C4—431no—
226C23×C4—431no—
227C23×C4—431no—
228C23×C4C4×D4311yescharacteristic
229C2×M16—1721no—
230#123—862no—
231#123—862no—
232C4×D4—1721no—
233C4×D4—1721no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—1721no—
240C2×C4⋊C4—1721no—
241C2×C22⋊C4—431no—
242C2×C22⋊C4—431no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4C4×D4311yescharacteristic
246C2×C22⋊C4C22×D4311yescharacteristic
247C2×C42—431no—
248C2×C42—861no—
249C4⋊C8—1721no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—861no—
253C22⋊C8—861no—
254C22⋊C8—1721no—
255#97—1721no—
256#95—21no—
257#95—861no—
258#95—861no—
259#95—861no—
260#95—861no—
261C24—431no—
262C24C2×C4×D4311yescharacteristic
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—1721no—
266C2×D4—1721no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—81no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—432no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—3441no—
283C22×C4—3441no—
284C22×C4—1721no—
285C22×C4—1721no—
286C22×C4D4×D4311yescharacteristic
287C22×C4D4×D4311yescharacteristic
288M16—3442no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—1721no—
292C2×C8—1721no—
293C4⋊C4—81no—
294C4⋊C4—864no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1722no—
299C22⋊C4—21no—
300C22⋊C4—41no—
301C22⋊C4—864no—
302C22⋊C4—3441no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C22⋊C4#1062187212yescomplemented
306C42—861no—
307C42—861no—
308C42—3441no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—861no—
314C23—861no—
315C23—861no—
316C23—1721no—
317C23—1721no—
318C23C22⋊C4×D4311yescharacteristic
319C23M16×D4311yescharacteristic
320C23C2×#1062187211yescharacteristic
321D4—1722no—
322D4—1722no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—82no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—862no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—3441no—
342C2×C4—3441no—
343C2×C4—3441no—
344C2×C4—1722no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1722no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1722no—
354C8—81no—
355C8—81no—
356C8—3441no—
357C8—3441no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—3441no—
368C22—1722no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22#1458286111yescharacteristic
373C22#99×D4311yescharacteristic
374C22#1458288211yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—861no—
380C4—861no—
381C4—3441no—
382C4—1721no—
383C4—1722no—
384C4—1721no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—3441no—
390C2#1913293211yescharacteristic
391C2#1913623811yescharacteristic
392C2#1913624711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1326C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1326D43
hypocenterC43#11528
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1326

Complements

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

NH ≅ G/Ntype
4. #19132543C2semidirect
5. #19132524C2semidirect
6. #19132524C2semidirect
7. C43×#1326C2semidirect
87. C22×Dic43M16semidirect
96. C22⋊C4×C43M16semidirect
193. #1326D43semidirect
223. C43#11528semidirect
305. C22⋊C4#10621872semidirect

Maximal subgroups

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

subgroupindex
#191372632
#191329342
#191329302
#191325432
#191325242
C43×#13262
#1152843