Finite Group Databasebeta

← #25007077

Subgroups — #25007077

Order 11008.

486 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 71 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#19140283C211yesmaximal, characteristic
2#19134326C211yesmaximal, characteristic, complemented
3#19132926C211yesmaximal, characteristic, complemented
4#19132616C211yesmaximal, characteristic, complemented
5#19132593C211yesmaximal, characteristic
6#19132591C211yesmaximal, characteristic
7C43×#1351C211yesmaximal, characteristic, complemented
8C2×#13063314C411yescharacteristic, complemented
9C2×#13063281—21no—
10C2×#13063281C2211yescharacteristic
11#14582953—21no—
12#14582818C411yescharacteristic, complemented
13#14582817C411yescharacteristic, complemented
14#14582808C2211yescharacteristic
15#14582799—21no—
16#14582788—21no—
17#14582788—21no—
18#14582776—21no—
19#14582744C411yescharacteristic, complemented
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#393C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C23×Dic43D411yescharacteristic
30#13063314—41no—
31#13063314—41no—
32#13063281—24no—
33#13063281—41no—
34#13063281—41no—
35#13063281—42no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—41no—
38C2×Dic43⋊C4C2×C411yescharacteristic
39C2×Dic43⋊C4D411yescharacteristic
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43D411yescharacteristic
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—41no—
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51Dic43⋊C8—41no—
52C22⋊(C43⋊C8)—21no—
53#13063235—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C22×Q8×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C23×D43—21no—
66C2×Q8×C43—41no—
67C2×Q8×C43—81no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—41no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C2×C22⋊D43—42no—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C2×C22⋊D43—81no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—22no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—41no—
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C2×D172—41no—
89C2×D172—81no—
90C2×C8×C43—41no—
91C22⋊C4×C43—22no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—81no—
95C22⋊Dic43—22no—
96C22⋊Dic43—41no—
97C22⋊Dic43—41no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4—81no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106Dic43⋊C4—44no—
107Dic43⋊C4—81no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—42no—
113C4×Dic43—44no—
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×C43#13711yescharacteristic
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129Q8×C43—82no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C22⋊D43—82no—
144C22⋊D43—82no—
145C2×Dic43—22no—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—22no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—42no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163C2×Dic43#9911yescharacteristic
164C2×Dic43#9911yescharacteristic
165C2×Dic43#10412yes—
166D172—82no—
167C8×C43—81no—
168C43⋊C8—81no—
169#11758—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—81no—
179C22×C43C2×#9911yescharacteristic
180C22×C43#41711yescharacteristic
181C22×C43C2×#10411yescharacteristic
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C2×D43—81no—
188C2×D43—81no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—81no—
192C4×C43—82no—
193C4×C43—81no—
194Dic43—21no—
195Dic43—21no—
196Dic43—22no—
197Dic43—42no—
198Dic43—41no—
199Dic43—41no—
200Dic43—82no—
201#2610—431no—
202#1740—431no—
203#1464—431no—
204#1351—431no—
205#1351D4311yescharacteristic, complemented
206#1343—431no—
207#1343—431no—
208C2×C43—21no—
209C2×C43—21no—
210C2×C43—41no—
211C2×C43—41no—
212C2×C43#150411yescharacteristic
213C2×C43#212211yescharacteristic
214C2×C43#212611yescharacteristic
215D43—161no—
216C2×#124—431no—
217C2×#117—431no—
218C2×#117—861no—
219#432—861no—
220#395—431no—
221#394—431no—
222#393C2×D4311yescharacteristic
223#392—431no—
224#390—861no—
225#388—861no—
226#388—861no—
227#386—861no—
228#376—431no—
229#342—431no—
230#342—861no—
231#342C2×D4311yescharacteristic
232#324—861no—
233#323—431no—
234#323C2×D4311yescharacteristic
235C43#1175811yescharacteristic, complemented, Sylow
236C22×Q8C4×D4311yescharacteristic
237C22×D4—431no—
238C22×D4—861no—
239C23×C4—431no—
240#124—1721no—
241#124—1721no—
242#117—864no—
243#117—1721no—
244#117—1721no—
245#117—1722no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—1721no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—431no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4C22×D4311yescharacteristic
260C2×C42—431no—
261C2×C42—431no—
262C2×C42—861no—
263C2×C42—1721no—
264C4⋊C8—1721no—
265C22⋊C8—21no—
266C22⋊C8—861no—
267#97—1721no—
268#95—21no—
269#95—431no—
270#95—861no—
271#95—861no—
272#95C4×D4311yescharacteristic
273C24—861no—
274C24D4×D4311yescharacteristic
275C2×Q8—41no—
276C2×Q8—81no—
277C2×D4—3441no—
278C2×D4—3441no—
279C2×D4—1721no—
280C2×D4—1722no—
281C2×D4—1721no—
282C2×D4—1721no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—862no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—1721no—
297C22×C4C2×C4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C2×C8—41no—
300C2×C8—1721no—
301C4⋊C4—3441no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4—1724no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C22⋊C4—862no—
310C22⋊C4—3441no—
311C22⋊C4—1721no—
312C22⋊C4—1721no—
313C22⋊C4—1722no—
314C22⋊C4—1722no—
315C22⋊C4—1722no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C42—861no—
319C42—861no—
320C42—861no—
321C42—861no—
322C42—1722no—
323C42—1724no—
324C23—21no—
325C23—21no—
326C23—41no—
327C23—41no—
328C23—1721no—
329C23—1721no—
330C23—1721no—
331C23—1721no—
332C23—1721no—
333C23—1721no—
334C23—1721no—
335C23C22⋊C4×D4311yescharacteristic
336C23#1306335211yescharacteristic
337C23#1306335711yescharacteristic
338Q8—82no—
339D4—3442no—
340D4—3442no—
341D4—3442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—431no—
356C2×C4—431no—
357C2×C4—432no—
358C2×C4—862no—
359C2×C4—862no—
360C2×C4—862no—
361C2×C4—862no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—862no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—3441no—
370C2×C4—3441no—
371C2×C4—1722no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C8—81no—
377C8—3441no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—81no—
387C22—3441no—
388C22—3441no—
389C22—3441no—
390C22—3441no—
391C22—3441no—
392C22—3441no—
393C22—3441no—
394C22#99×D4311yescharacteristic
395C22#1458289911yescharacteristic
396C22#104×D4311yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—82no—
401C4—81no—
402C4—861no—
403C4—861no—
404C4—862no—
405C4—3442no—
406C4—1722no—
407C4—1721no—
408C4—1721no—
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—6881no—
414C2#1913309811yescharacteristic
415C2#1913624311yescharacteristic
416C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1351C2
socleC22×C43C2×#99
prime radical#14582808C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1351D43
hypocenterC43#11758
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
2. #19134326C2semidirect
3. #19132926C2semidirect
4. #19132616C2semidirect
7. C43×#1351C2semidirect
8. C2×#13063314C4semidirect
12. #14582818C4semidirect
13. #14582817C4semidirect
19. #14582744C4semidirect
205. #1351D43semidirect
235. C43#11758semidirect

Maximal subgroups

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

subgroupindex
#191402832
#191343262
#191329262
#191326162
#191325932
#191325912
C43×#13512
#1175843