Finite Group Databasebeta

← #24994046

Subgroups — #24994046

Order 11008.

644 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 97 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#19140070C211yesmaximal, characteristic
2#19136950C211yesmaximal, characteristic, complemented
3#19133112C211yesmaximal, characteristic
4#19133110C211yesmaximal, characteristic
5#19132924C211yesmaximal, characteristic, complemented
6#19132481C211yesmaximal, characteristic, complemented
7C43×#1297C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063281—21no—
10C22×Dic43⋊C4C2211yescharacteristic
11#14582863C2211yescharacteristic
12#14582839C412yescomplemented
13#14582817C412yescomplemented
14#14582790—22no—
15#14582776—21no—
16#14582776—21no—
17C4×Dic43⋊C4—22no—
18#14582750—22no—
19C22⋊C4×Dic43—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21#14582634—22no—
22#14582632—22no—
23#14582624—22no—
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C23×Dic43D411yescharacteristic
30C23×Dic43D411yescharacteristic
31C2×#10621877—21no—
32#13063299—21no—
33#13063299—21no—
34#13063299—21no—
35#13063299—21no—
36#13063281—28no—
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—22no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4C2×C412yes—
44C2×Dic43⋊C4D412yes—
45C2×C22⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—22no—
48C2×(C2×D43)⋊C4—22no—
49C2×C4×Dic43—22no—
50C2×C4×Dic43—22no—
51C2×C4×Dic43—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95D412yes—
58C23×C4×C43C2311yescharacteristic
59C2×M16×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43C2×C412yes—
67#95×C43D412yes—
68C24×C43C2×D411yescharacteristic
69C23×D43—21no—
70C22×C4×C43—22no—
71C22×C4×C43—22no—
72C22×C4×C43—81no—
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—44no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C22×Dic43—24no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—81no—
90C22×Dic43C22⋊C412yes—
91C22×Dic43C22⋊C412yes—
92C2×D172—21no—
93C2×D172—21no—
94C2×D172—81no—
95M16×C43—81no—
96C2×C8×C43—41no—
97C22⋊C4×C43—24no—
98C22⋊C4×C43—42no—
99C42×C43—81no—
100C42×C43—81no—
101C22⋊Dic43—24no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—44no—
105(C2×D43)⋊C4—82no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108Dic43⋊C4—28no—
109Dic43⋊C4—22no—
110Dic43⋊C4—22no—
111Dic43⋊C4—22no—
112Dic43⋊C4—22no—
113C4×Dic43—28no—
114C4×Dic43—81no—
115C4×Dic43—82no—
116#10621877—81no—
117C2×C43⋊C8—41no—
118C23×C43—22no—
119C23×C43—22no—
120C23×C43—41no—
121C23×C43C2×C22⋊C411yescharacteristic
122C23×C43#12011yescharacteristic
123C23×C43#12311yescharacteristic
124C22×D43—42no—
125C22×D43—42no—
126C22×D43—41no—
127C22×D43—42no—
128C2×C4×C43—24no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C22⋊D43—82no—
145C22⋊D43—82no—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—24no—
149C2×Dic43—22no—
150C2×Dic43—22no—
151C2×Dic43—24no—
152C2×Dic43—22no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—41no—
159C2×Dic43—81no—
160C2×Dic43#10414yes—
161D172—81no—
162D172—81no—
163C8×C43—81no—
164C43⋊C8—81no—
165#9410—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—44no—
174C22×C43#38611yescharacteristic
175C22×C43C2×#10412yes—
176C22×C43#45412yes—
177C2×D43—84no—
178C2×D43—81no—
179C2×D43—81no—
180C2×D43—81no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—44no—
186C4×C43—82no—
187Dic43—24no—
188Dic43—44no—
189Dic43—42no—
190Dic43—81no—
191#2591—431no—
192#2274—431no—
193#1507—431no—
194#1507—431no—
195#1463—431no—
196#1297—431no—
197#1297D4311yescharacteristic, complemented
198C2×C43—22no—
199C2×C43—22no—
200C2×C43—41no—
201C2×C43#188811yescharacteristic
202C2×C43#189611yescharacteristic
203C2×C43#191311yescharacteristic
204D43—161no—
205C2×#121—431no—
206C2×#117—861no—
207C22×C4⋊C4—431no—
208#407—431no—
209#407C2×D4311yescharacteristic
210#400—432no—
211#394—432no—
212#388—862no—
213#386—861no—
214#386—861no—
215C4×C4⋊C4—862no—
216C4×C4⋊C4—862no—
217C4×C22⋊C4—431no—
218C4×C22⋊C4—861no—
219C4×C22⋊C4C2×D4311yescharacteristic
220C4×C22⋊C4C2×D4311yescharacteristic
221#327—862no—
222#327—862no—
223#324—862no—
224C43#941011yescharacteristic, complemented, Sylow
225C22×D4—431no—
226C22×D4—861no—
227C23×C4—431no—
228C23×C4—431no—
229C23×C4C22×D4311yescharacteristic
230C2×M16—21no—
231C2×M16—861no—
232#121—861no—
233#121—861no—
234#121—861no—
235#121—861no—
236#117—868no—
237C2×C4⋊C4—432no—
238C2×C4⋊C4—432no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—862no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—862no—
249C2×C22⋊C4—862no—
250C2×C22⋊C4—861no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—862no—
254C2×C42—862no—
255C2×C42—861no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—861no—
259C22⋊C8—861no—
260#95—432no—
261#95—862no—
262#95—862no—
263#95—862no—
264#95C4×D4312yes—
265#95D17212yes—
266C24—861no—
267C24D4×D4311yescharacteristic
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—3441no—
271C2×D4—1724no—
272C2×D4—1721no—
273C2×D4—1721no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—81no—
277C22×C4—432no—
278C22×C4—432no—
279C22×C4—864no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—862no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—3441no—
287C22×C4C2×C4×D4311yescharacteristic
288C22×C4C2×D17211yescharacteristic
289C22×C4#1062189811yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4#1062190211yescharacteristic
293M16—81no—
294M16—3441no—
295C2×C8—41no—
296C2×C8—1721no—
297C4⋊C4—868no—
298C4⋊C4—862no—
299C4⋊C4—862no—
300C4⋊C4—862no—
301C4⋊C4—862no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C22⋊C4—24no—
305C22⋊C4—42no—
306C22⋊C4—864no—
307C22⋊C4—3442no—
308C22⋊C4—1724no—
309C22⋊C4—1721no—
310C22⋊C4—1721no—
311C42—81no—
312C42—81no—
313C42—868no—
314C42—3441no—
315C42—3442no—
316C23—22no—
317C23—22no—
318C23—41no—
319C23—1722no—
320C23—1722no—
321C23—1722no—
322C23—1721no—
323C23C22⋊C4×D4311yescharacteristic
324C23#1306329511yescharacteristic
325C23#1306331011yescharacteristic
326D4—3441no—
327D4—3441no—
328D4—3442no—
329D4—3442no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—434no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—864no—
346C2×C4—862no—
347C2×C4—862no—
348C2×C4—864no—
349C2×C4—862no—
350C2×C4—3441no—
351C2×C4—1722no—
352C2×C4—1721no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4#1306328711yescharacteristic
358C2×C4C4×D17211yescharacteristic
359C2×C4#1306329811yescharacteristic
360C2×C4#1306330011yescharacteristic
361C8—81no—
362C8—3441no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—3444no—
372C22—3441no—
373C22—3441no—
374C22—3441no—
375C22#1458277711yescharacteristic
376C22#104×D4312yes—
377C22#1458307312yes—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—82no—
384C4—864no—
385C4—3441no—
386C4—1724no—
387C4—1722no—
388C2—22no—
389C2—22no—
390C2—41no—
391C2—6881no—
392C2#1913499711yescharacteristic
393C2#1913503711yescharacteristic
394C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1297C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1297D43
hypocenterC43#9410
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #19136950C2semidirect
5. #19132924C2semidirect
6. #19132481C2semidirect
7. C43×#1297C2semidirect
12. #14582839C4semidirect
13. #14582817C4semidirect
197. #1297D43semidirect
224. C43#9410semidirect

Maximal subgroups

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

subgroupindex
#191400702
#191369502
#191331122
#191331102
#191329242
#191324812
C43×#12972
#941043