Finite Group Databasebeta

← #25007156

Subgroups — #25007156

Order 11008.

544 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 83 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#19139492C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic, complemented
3#19132594C212yesmaximal, complemented
4#19132591C212yesmaximal, complemented
5C4×#99×C43C211yesmaximal, characteristic, complemented
6C2×#13063296—21no—
7C2×C4×D172C411yescharacteristic, complemented
8#14582863—21no—
9#14582824C411yescharacteristic, complemented
10#14582824C2211yescharacteristic
11#14582808C411yescharacteristic, complemented
12#14582808C2211yescharacteristic
13#14582778—21no—
14#14582778—21no—
15#14582765C411yescharacteristic, complemented
16#14582756—21no—
17#14582625—21no—
18#14582623C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C2×#99×C43—21no—
21C4×C22⋊C4×C43—21no—
22C43×#342C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C22⋊D43—21no—
26C22×C4×D43—21no—
27C2×#10621877—41no—
28#13063296—44no—
29C4×D172—41no—
30C4×D172—41no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C22⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)—41no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×D4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C4×D4×C43—41no—
49C4×D4×C43—41no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43C2311yescharacteristic
54C2×C42×C43—41no—
55C2×C42×C43C2×C411yescharacteristic
56#99×C43—24no—
57#95×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C2×D411yescharacteristic
60C23×D43—21no—
61C2×D4×C43—22no—
62C2×D4×C43—22no—
63C2×D4×C43—41no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—42no—
69C22×C4×C43—81no—
70C22×C4×C43—81no—
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—42no—
77C2×C22⋊D43—42no—
78C2×C22⋊D43—42no—
79C2×C22⋊D43—42no—
80C2×C22⋊D43—81no—
81C2×C22⋊D43—81no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C2×D172—42no—
86C2×D172—41no—
87C2×C4×D43—42no—
88C2×C4×D43—42no—
89C2×C4×D43—42no—
90C4⋊C4×C43—41no—
91C22⋊C4×C43—24no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—42no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—82no—
98C22⋊Dic43—42no—
99C22⋊Dic43—42no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—81no—
103(C2×D43)⋊C4—81no—
104C4⋊Dic43—42no—
105C4⋊Dic43—41no—
106#10621877—82no—
107C2×C43⋊C8—42no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43C2×C22⋊C411yescharacteristic
118C23×C43AGL(1,ℤ/8)12yes—
119C22×D43—22no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126D4×C43—44no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—44no—
139C2×C4×C43—81no—
140C2×C4×C43—81no—
141C2×C4×C43—82no—
142C2×C4×C43—82no—
143C2×C4×C43#9911yescharacteristic
144C2×C4×C43#9911yescharacteristic
145C2×C4×C43#10412yes—
146C22⋊D43—84no—
147C22⋊D43—84no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157D172—42no—
158D172—42no—
159C4×D43—84no—
160C43⋊C8—82no—
161#11774—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—22no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43C2×#9911yescharacteristic
175C22×C43#41811yescharacteristic
176C22×C43C2×#10411yescharacteristic
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—22no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—41no—
190C4×C43—84no—
191Dic43—81no—
192Dic43—81no—
193Dic43—81no—
194#2535—431no—
195C4×#99D4311yescharacteristic, complemented
196#1465—431no—
197#1344—432no—
198#1343—432no—
199C2×C43—21no—
200C2×C43—21no—
201C2×C43—42no—
202C2×C43—81no—
203C2×C43#150711yescharacteristic
204C2×C43#212011yescharacteristic
205C2×C43#212711yescharacteristic
206D43—82no—
207C2×#121—861no—
208C2×C4×D4—431no—
209C2×C4×D4C2×D4311yescharacteristic
210C2×#99—21no—
211#407—861no—
212#397—431no—
213#397—431no—
214#392—431no—
215#392—431no—
216#386—861no—
217#386—861no—
218#382—431no—
219#380—861no—
220C4×C22⋊C4—21no—
221#342C2×D4312yes—
222#324—861no—
223#323—432no—
224C43#1177411yescharacteristic, complemented, Sylow
225C22×D4—431no—
226C22×D4—861no—
227C22×D4—861no—
228C22×D4C22⋊D4311yescharacteristic
229C23×C4—861no—
230C23×C4D17211yescharacteristic
231C23×C4C22⋊D4311yescharacteristic
232C2×M16—1721no—
233#121—1724no—
234C4×D4—41no—
235C4×D4—41no—
236C4×D4—1721no—
237C4×D4—1721no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4D17211yescharacteristic
241C2×C22⋊C4—22no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4C4×D4311yescharacteristic
248C2×C22⋊C4C22×D4311yescharacteristic
249C2×C42—41no—
250C2×C42C4×D4311yescharacteristic
251#99—24no—
252C22⋊C8—862no—
253C22⋊C8—1721no—
254#95—41no—
255#95—431no—
256#95—431no—
257#95—861no—
258#95—861no—
259#95—861no—
260C24—861no—
261C24(C2×D43)⋊C411yescharacteristic
262C24C2×C22⋊D4311yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—3441no—
267C2×D4—3441no—
268C2×D4—1721no—
269C2×D4—1722no—
270C2×D4—1722no—
271C2×D4—1722no—
272C2×D4—1722no—
273C2×D4—1722no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—1722no—
285C22×C4—1722no—
286C22×C4—1722no—
287C22×C4(C2×D43)⋊C411yescharacteristic
288C22×C4(C2×D43)⋊C411yescharacteristic
289C22×C4(C2×D43)⋊C411yescharacteristic
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4C2×D17211yescharacteristic
292M16—3442no—
293C2×C8—1722no—
294C4⋊C4—41no—
295C4⋊C4—1721no—
296C4⋊C4—1722no—
297C22⋊C4—24no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—3441no—
302C22⋊C4—3441no—
303C22⋊C4—1722no—
304C22⋊C4—1722no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C42—21no—
308C42—21no—
309C42—82no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—862no—
320C23—1721no—
321C23—1721no—
322C23—1721no—
323C23—1721no—
324C23—1721no—
325C23—1721no—
326C23C2×(C2×D43)⋊C411yescharacteristic
327C23#1306335012yes—
328D4—44no—
329D4—3444no—
330D4—3444no—
331D4—1722no—
332D4—1722no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—44no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—3444no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4#1306323911yescharacteristic
360C2×C4#1306323911yescharacteristic
361C2×C4#1306325312yes—
362C8—3442no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—3441no—
376C22—3441no—
377C22—3441no—
378C22—3441no—
379C22—1722no—
380C22—1722no—
381C22—1722no—
382C22C2×#1306323911yescharacteristic
383C22#1458290311yescharacteristic
384C22C2×#1306325311yescharacteristic
385C4—21no—
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—84no—
392C4—3441no—
393C4—3441no—
394C4—3441no—
395C2—21no—
396C2—21no—
397C2—42no—
398C2—81no—
399C2—3442no—
400C2#1913311011yescharacteristic
401C2#1913623411yescharacteristic
402C2#1913626211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC4×#99×C43C2
socleC22×C43C2×#99
prime radical#19139492C2
cosocleC2×C22⋊C4×C43C23
hypercenterC4×#99D43
hypocenterC43#11774
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #19132933C2semidirect
3. #19132594C2semidirect
4. #19132591C2semidirect
5. C4×#99×C43C2semidirect
7. C2×C4×D172C4semidirect
9. #14582824C4semidirect
11. #14582808C4semidirect
15. #14582765C4semidirect
195. C4×#99D43semidirect
224. C43#11774semidirect

Maximal subgroups

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

subgroupindex
#191394922
#191329332
#191325942
#191325912
C4×#99×C432
#1177443