Finite Group Databasebeta

← #25007364

Subgroups — #25007364

Order 11008.

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

normal subgroups only

This group has 582 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#19137874C211yesmaximal, characteristic
2#19134583C211yesmaximal, characteristic, complemented
3#19132620C212yesmaximal, complemented
4#19132593C212yesmaximal, complemented
5C43×#1465C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic, complemented
7C2×C4×C22⋊D43—21no—
8C2×C4×C22⋊D43—21no—
9C2×#13063240—21no—
10#14582835C411yescharacteristic, complemented
11#14582835C2211yescharacteristic
12#14582834—21no—
13#14582808C411yescharacteristic, complemented
14#14582808C2211yescharacteristic
15#14582807—21no—
16#14582759—21no—
17#14582745C411yescharacteristic, complemented
18#14582666C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#324—21no—
22C43×#323C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C22⋊D43—21no—
26C22×C4×D43—21no—
27C4×D172—41no—
28C4×D172—41no—
29C4×C22⋊D43—44no—
30C4×C22⋊D43—44no—
31C2×C4⋊Dic43—41no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—22no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×C4×Dic43—21no—
42#13063240—42no—
43C43⋊#95—21no—
44C43⋊#95—41no—
45C43⋊#95C2×C411yescharacteristic
46C43⋊#95C2×C411yescharacteristic
47C22×D4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C2×M16×C43—41no—
51C4×D4×C43—41no—
52C4×D4×C43—41no—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43C2×C411yescharacteristic
55C2×C22⋊C4×C43C2311yescharacteristic
56C2×C42×C43C2×C411yescharacteristic
57C22⋊C8×C43—22no—
58C22⋊C8×C43—41no—
59C24×C43C22⋊C411yescharacteristic
60C24×C43C2×D411yescharacteristic
61C23×D43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—41no—
65C2×D4×C43—41no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—42no—
71C22×C4×C43—42no—
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C2×C22⋊D43—42no—
78C2×C22⋊D43—42no—
79C2×C22⋊D43—42no—
80C2×C22⋊D43—42no—
81C2×C22⋊D43—42no—
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—42no—
88C2×D172—42no—
89C2×D172—41no—
90C2×C4×D43—42no—
91C2×C4×D43—42no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94M16×C43—82no—
95C2×C8×C43—42no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C42×C43—21no—
100C42×C43—21no—
101C22⋊Dic43—42no—
102C22⋊Dic43—42no—
103C22⋊Dic43—42no—
104C22⋊Dic43—42no—
105(C2×D43)⋊C4—42no—
106(C2×D43)⋊C4—42no—
107(C2×D43)⋊C4—42no—
108C4⋊Dic43—41no—
109C4⋊Dic43—82no—
110Dic43⋊C4—42no—
111Dic43⋊C4—42no—
112C4×Dic43—24no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43C2×C22⋊C411yescharacteristic
123C23×C43AGL(1,ℤ/8)11yescharacteristic
124C23×C43#13711yescharacteristic
125C22×D43—22no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132D4×C43—42no—
133D4×C43—42no—
134C2×C4×C43—22no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43#9911yescharacteristic
149C2×C4×C43#9911yescharacteristic
150C22⋊D43—44no—
151C22⋊D43—44no—
152C22⋊D43—48no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—82no—
163C2×Dic43—82no—
164C2×Dic43—82no—
165D172—42no—
166D172—42no—
167C4×D43—82no—
168C4×D43—82no—
169C8×C43—82no—
170#11821—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—42no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43C2×#9911yescharacteristic
186C22×C43#41711yescharacteristic
187C22×C43#42111yescharacteristic
188C2×D43—42no—
189C2×D43—42no—
190C2×D43—42no—
191C2×D43—81no—
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C4×C43—21no—
196C4×C43—41no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43#35312yes—
201Dic43—42no—
202Dic43—42no—
203Dic43—81no—
204Dic43—162no—
205#2397—431no—
206#1799—431no—
207#1465D4311yescharacteristic, complemented
208#1352—432no—
209#1343—432no—
210C2×C43—21no—
211C2×C43—21no—
212C2×C43—41no—
213C2×C43—41no—
214C2×C43—81no—
215C2×C43#151311yescharacteristic
216C2×C43#212011yescharacteristic
217C2×C43C2×#35311yescharacteristic
218D43—82no—
219C2×C4×D4—431no—
220C2×C4×D4—861no—
221C2×C4×D4—861no—
222C2×C4×D4C2×D4311yescharacteristic
223C2×#99—861no—
224#407—21no—
225#399—431no—
226#399—431no—
227#399—861no—
228#392—431no—
229#392—431no—
230#392—861no—
231#380—861no—
232#376—431no—
233#342—432no—
234#324—21no—
235#323C2×D4312yes—
236C43#1182111yescharacteristic, complemented, Sylow
237C22×D4—431no—
238C22×D4—861no—
239C22×D4—861no—
240C22×D4D17211yescharacteristic
241C23×C4—861no—
242C23×C4D17211yescharacteristic
243C23×C4C22⋊D4311yescharacteristic
244C2×M16—41no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—1721no—
248C4×D4—1721no—
249C4×D4—1724no—
250C4×D4—1724no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—1721no—
255C2×C4⋊C4C22⋊D4311yescharacteristic
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—862no—
262C2×C22⋊C4C4×D4311yescharacteristic
263C2×C22⋊C4C22×D4311yescharacteristic
264C2×C42—861no—
265C2×C42C4×D4311yescharacteristic
266#99—1722no—
267C22⋊C8—22no—
268C22⋊C8—41no—
269#95—431no—
270#95—431no—
271#95—861no—
272#95—1721no—
273C24—861no—
274C24(C2×D43)⋊C411yescharacteristic
275C24C2×D17211yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—1721no—
281C2×D4—1722no—
282C2×D4—1722no—
283C2×D4—1722no—
284C2×D4—1722no—
285C2×D4—1722no—
286C2×D4—1722no—
287C2×D4—1721no—
288C2×D4—1721no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—1722no—
299C22×C4—1722no—
300C22×C4—1722no—
301C22×C4—1721no—
302C22×C4—1721no—
303C22×C4(C2×D43)⋊C411yescharacteristic
304C22×C4(C2×D43)⋊C411yescharacteristic
305C22×C4(C2×D43)⋊C411yescharacteristic
306C22×C4C2×C4×D4311yescharacteristic
307C22×C4C2×C22⋊D4311yescharacteristic
308M16—82no—
309C2×C8—42no—
310C4⋊C4—41no—
311C4⋊C4—3442no—
312C4⋊C4—1721no—
313C4⋊C4—1722no—
314C4⋊C4—1722no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—1722no—
318C22⋊C4—1722no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1722no—
322C22⋊C4—1722no—
323C22⋊C4—1722no—
324C42—21no—
325C42—21no—
326C42—864no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—862no—
337C23—1721no—
338C23—1721no—
339C23—1721no—
340C23—1721no—
341C23—1721no—
342C23—1721no—
343C23C2×(C2×D43)⋊C411yescharacteristic
344C23#1306335311yescharacteristic
345C23#1306335811yescharacteristic
346D4—42no—
347D4—42no—
348D4—1722no—
349D4—1722no—
350D4—1724no—
351D4—1724no—
352D4—1728no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—862no—
368C2×C4—862no—
369C2×C4—3442no—
370C2×C4—3442no—
371C2×C4—3442no—
372C2×C4—3442no—
373C2×C4—3442no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4#1306323911yescharacteristic
382C2×C4#1306323911yescharacteristic
383C8—82no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—81no—
398C22—3441no—
399C22—3441no—
400C22—3441no—
401C22—3441no—
402C22—1722no—
403C22—1722no—
404C22—1722no—
405C22C2×#1306323911yescharacteristic
406C22#1458290111yescharacteristic
407C22#1458291511yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—3441no—
414C4—1722no—
415C4—1722no—
416C4—6882no—
417C4#1458269112yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—3442no—
424C2#1913313911yescharacteristic
425C2#1913623711yescharacteristic
426C2C2×#1458269111yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radical#19137874C2
cosocleC2×C22⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11821
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #19134583C2semidirect
3. #19132620C2semidirect
4. #19132593C2semidirect
5. C43×#1465C2semidirect
6. C2×C4×D172C4semidirect
10. #14582835C4semidirect
13. #14582808C4semidirect
17. #14582745C4semidirect
207. #1465D43semidirect
236. C43#11821semidirect

Maximal subgroups

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

subgroupindex
#191378742
#191345832
#191326202
#191325932
C43×#14652
#1182143