Finite Group Databasebeta

← #25007151

Subgroups — #25007151

Order 11008.

482 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 73 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#19138896C211yesmaximal, characteristic
2#19134382C211yesmaximal, characteristic
3#19132934C211yesmaximal, characteristic
4#19132596C211yesmaximal, characteristic, complemented
5#19132595C211yesmaximal, characteristic, complemented
6#19132594C211yesmaximal, characteristic, complemented
7C43×#1344C211yesmaximal, characteristic, complemented
8C2×#13063307—21no—
9C2×(C22⋊D43)⋊C4C2211yescharacteristic
10C2×C4⋊C4×D43C411yescharacteristic, complemented
11#14582953—21no—
12C2×#13063239—21no—
13#14582831C411yescharacteristic, complemented
14#14582830C411yescharacteristic, complemented
15#14582824C2211yescharacteristic
16#14582796—21no—
17#14582761—21no—
18#14582758C411yescharacteristic, complemented
19#14582757—21no—
20C22⋊C4×Dic43—21no—
21#14582666C2211yescharacteristic
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#397C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C22×C4×D43—21no—
30C22×C4×D43C2×C411yescharacteristic
31#13063307—42no—
32#13063307—42no—
33(C22⋊D43)⋊C4—41no—
34(C22⋊D43)⋊C4—41no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4C2×C411yescharacteristic
41C4⋊C4×D43—41no—
42C4⋊C4×D43—41no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4D411yescharacteristic
47C2×C4×Dic43—41no—
48C2×C4×Dic43D411yescharacteristic
49Dic43⋊C8—41no—
50#13063239—24no—
51C22⋊(C43⋊C8)—21no—
52#13063235—41no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—41no—
57C43⋊#95C2×C411yescharacteristic
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43C2311yescharacteristic
62C22⋊C8×C43—21no—
63#95×C43—21no—
64#95×C43C2×C411yescharacteristic
65C24×C43C2×D411yescharacteristic
66C23×D43C22⋊C411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—22no—
75C2×C22⋊D43—41no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—41no—
81C22×Dic43—42no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—42no—
88C2×C4×D43—42no—
89C2×C4×D43—42no—
90C2×C4×D43—42no—
91C2×C8×C43—41no—
92C4⋊C4×C43—41no—
93C22⋊C4×C43—22no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊Dic43—22no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—42no—
104C4⋊Dic43—42no—
105C4⋊Dic43—41no—
106Dic43⋊C4—41no—
107Dic43⋊C4—42no—
108Dic43⋊C4—42no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43—82no—
114C2×C43⋊C8—41no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43C2×C22⋊C411yescharacteristic
120C23×C43AGL(1,ℤ/8)11yescharacteristic
121C23×C43AGL(1,ℤ/8)11yescharacteristic
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43#10412yes—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—42no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C22⋊D43—42no—
141C22⋊D43—42no—
142C2×Dic43—22no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—42no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—42no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159C2×Dic43#9911yescharacteristic
160C2×Dic43#9911yescharacteristic
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—84no—
164C8×C43—81no—
165C43⋊C8—81no—
166#11773—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—81no—
176C22×C43C2×#9911yescharacteristic
177C22×C43#41811yescharacteristic
178C22×C43C2×#10411yescharacteristic
179C2×D43—22no—
180C2×D43—42no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—42no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—81no—
187C4×C43—82no—
188C4×C43—81no—
189Dic43—21no—
190Dic43—41no—
191Dic43—41no—
192Dic43—81no—
193Dic43—82no—
194Dic43—81no—
195Dic43#35212yes—
196#2486—431no—
197C4×#99—431no—
198#1466—431no—
199#1344—431no—
200#1344—431no—
201#1344—431no—
202#1344D4311yescharacteristic, complemented
203C2×C43—21no—
204C2×C43—21no—
205C2×C43—41no—
206C2×C43—41no—
207C2×C43#150711yescharacteristic
208C2×C43C2×#35211yescharacteristic
209C2×C43#212911yescharacteristic
210D43—42no—
211C2×#123—861no—
212C2×C4×D4—431no—
213C22×C4⋊C4—431no—
214#432—861no—
215C2×#99—861no—
216#398—431no—
217#398—431no—
218#397—431no—
219#397C2×D4311yescharacteristic
220#389—861no—
221#381—861no—
222#380—431no—
223#380—861no—
224C4×C22⋊C4—861no—
225#342—431no—
226#342C2×D4311yescharacteristic
227#323—431no—
228#323—861no—
229#323C2×D4311yescharacteristic
230C43#1177311yescharacteristic, complemented, Sylow
231C22×D4—431no—
232C23×C4—431no—
233C23×C4—431no—
234C23×C4—861no—
235#123—1722no—
236#123—1722no—
237C4×D4—1721no—
238C4×D4—1721no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—1721no—
246C2×C4⋊C4—1721no—
247C2×C4⋊C4C4×D4311yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—431no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4C22×D4311yescharacteristic
255C2×C42—431no—
256C2×C42—1721no—
257C4⋊C8—1721no—
258#99—864no—
259C22⋊C8—21no—
260C22⋊C8—861no—
261#97—1721no—
262#95—21no—
263#95—431no—
264#95—861no—
265#95—861no—
266#95—861no—
267#95—1721no—
268#95C4×D4311yescharacteristic
269C24—431no—
270C24D4×D4311yescharacteristic
271C2×D4—862no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—1721no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—1722no—
288C22×C4—1722no—
289C22×C4—1722no—
290C22×C4—1722no—
291C22×C4—1722no—
292C22×C4—1721no—
293C22×C4C2×C4×D4311yescharacteristic
294C22×C4D4×D4311yescharacteristic
295C2×C8—41no—
296C2×C8—1721no—
297C4⋊C4—41no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C4⋊C4—1722no—
303C4⋊C4—1722no—
304C4⋊C4—1722no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—862no—
311C22⋊C4—1721no—
312C22⋊C4—1722no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C42—861no—
317C42—861no—
318C42—3442no—
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—432no—
324C23—861no—
325C23—861no—
326C23—1721no—
327C23—1721no—
328C23C22⋊C4×D4311yescharacteristic
329C23#1306334911yescharacteristic
330C23#1306335211yescharacteristic
331D4—1722no—
332D4—1722no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—431no—
347C2×C4—431no—
348C2×C4—862no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—3444no—
354C2×C4—3441no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1722no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C8—81no—
369C8—3441no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—862no—
380C22—1722no—
381C22—1722no—
382C22—1721no—
383C22—1721no—
384C22#99×D4311yescharacteristic
385C22#1458290211yescharacteristic
386C22#104×D4311yescharacteristic
387C4—41no—
388C4—41no—
389C4—81no—
390C4—82no—
391C4—81no—
392C4—432no—
393C4—861no—
394C4—3441no—
395C4—3442no—
396C4—3441no—
397C4—1721no—
398C4—1721no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—1722no—
404C2#1913310911yescharacteristic
405C2#352×D4311yescharacteristic
406C2#1913626811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1344C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1344D43
hypocenterC43#11773
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #19132596C2semidirect
5. #19132595C2semidirect
6. #19132594C2semidirect
7. C43×#1344C2semidirect
10. C2×C4⋊C4×D43C4semidirect
13. #14582831C4semidirect
14. #14582830C4semidirect
18. #14582758C4semidirect
202. #1344D43semidirect
230. C43#11773semidirect

Maximal subgroups

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

subgroupindex
#191388962
#191343822
#191329342
#191325962
#191325952
#191325942
C43×#13442
#1177343