Finite Group Databasebeta

← #24994066

Subgroups — #24994066

Order 11008.

552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137195C211yesmaximal, characteristic, complemented
3#19133112C211yesmaximal, characteristic
4#19133110C211yesmaximal, characteristic
5#19132924C211yesmaximal, characteristic, complemented
6#19132481C211yesmaximal, characteristic, complemented
7C43×#1297C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C22×Dic43⋊C4C2211yescharacteristic
10#14582863C2211yescharacteristic
11#14582839C412yescomplemented
12#14582817C412yescomplemented
13#14582790—22no—
14#14582783—22no—
15#14582781—22no—
16#14582776—21no—
17#14582776—21no—
18#14582760—21no—
19#14582757—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—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4C2×C412yes—
43C2×Dic43⋊C4D412yes—
44C2×C22⋊Dic43—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4—22no—
48C2×C4×Dic43—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C43⋊#95—22no—
52C43⋊#95—24no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95D412yes—
56C23×C4×C43C2311yescharacteristic
57C2×M16×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C42×C43—21no—
61C2×C42×C43—21no—
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64#95×C43C2×C412yes—
65#95×C43D412yes—
66C24×C43C2×D411yescharacteristic
67C23×D43—21no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—81no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C2×C22⋊D43—44no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—22no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—42no—
87C22×Dic43—81no—
88C22×Dic43C22⋊C412yes—
89C22×Dic43C22⋊C412yes—
90C2×D172—21no—
91C2×D172—21no—
92C2×D172—81no—
93M16×C43—81no—
94C2×C8×C43—41no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—42no—
97C42×C43—81no—
98C42×C43—81no—
99C22⋊Dic43—42no—
100(C2×D43)⋊C4—44no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—82no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106Dic43⋊C4—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—22no—
109Dic43⋊C4—22no—
110Dic43⋊C4—82no—
111C4×Dic43—81no—
112#10621877—81no—
113C2×C43⋊C8—41no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—41no—
117C23×C43C2×C22⋊C411yescharacteristic
118C23×C43#12011yescharacteristic
119C23×C43#12311yescharacteristic
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—41no—
123C22×D43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C22⋊D43—82no—
141C22⋊D43—82no—
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—41no—
154C2×Dic43—42no—
155C2×Dic43—81no—
156D172—81no—
157D172—81no—
158C8×C43—81no—
159C43⋊C8—81no—
160#9414—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—44no—
169C22×C43#38611yescharacteristic
170C22×C43#42112yes—
171C22×C43#45412yes—
172C2×D43—84no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—82no—
181C4×C43—82no—
182Dic43—42no—
183Dic43—42no—
184Dic43—82no—
185Dic43—81no—
186#2591—431no—
187#2313—431no—
188#1507—431no—
189#1507—431no—
190#1463—431no—
191#1297—431no—
192#1297D4311yescharacteristic, complemented
193C2×C43—22no—
194C2×C43—22no—
195C2×C43—41no—
196C2×C43#188811yescharacteristic
197C2×C43#189711yescharacteristic
198C2×C43#191311yescharacteristic
199D43—161no—
200C2×#121—431no—
201C22×C4⋊C4—431no—
202#407—431no—
203#407C2×D4311yescharacteristic
204#400—432no—
205#394—432no—
206#388—862no—
207#387—862no—
208#387—862no—
209#386—861no—
210#386—861no—
211#381—861no—
212#380—861no—
213C4×C22⋊C4—431no—
214C4×C22⋊C4C2×D4311yescharacteristic
215C4×C22⋊C4C2×D4311yescharacteristic
216#327—862no—
217#327—862no—
218#324—862no—
219C43#941411yescharacteristic, complemented, Sylow
220C22×D4—431no—
221C22×D4—861no—
222C23×C4—431no—
223C23×C4—431no—
224C23×C4C22×D4311yescharacteristic
225C2×M16—21no—
226C2×M16—861no—
227#121—861no—
228#121—861no—
229#121—861no—
230#121—861no—
231C2×C4⋊C4—432no—
232C2×C4⋊C4—432no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—862no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—862no—
242C2×C22⋊C4—862no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—861no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—861no—
251C22⋊C8—861no—
252#95—432no—
253#95—862no—
254#95—862no—
255#95—862no—
256#95—864no—
257#95C4×D4312yes—
258#95D17212yes—
259C24—861no—
260C24D4×D4311yescharacteristic
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—3441no—
264C2×D4—1724no—
265C2×D4—1721no—
266C2×D4—1721no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—81no—
270C22×C4—432no—
271C22×C4—432no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—862no—
278C22×C4—3441no—
279C22×C4—1722no—
280C22×C4C2×C4×D4311yescharacteristic
281C22×C4C2×D17211yescharacteristic
282C22×C4#1062189811yescharacteristic
283C22×C4D4×D4311yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4#1062190211yescharacteristic
286M16—81no—
287M16—3441no—
288C2×C8—41no—
289C2×C8—1721no—
290C4⋊C4—862no—
291C4⋊C4—862no—
292C4⋊C4—862no—
293C4⋊C4—862no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—3442no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—3442no—
300C22⋊C4—1724no—
301C22⋊C4—1722no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C42—81no—
305C42—81no—
306C42—3441no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23—1722no—
311C23—1722no—
312C23—1722no—
313C23—1721no—
314C23C22⋊C4×D4311yescharacteristic
315C23#1306329511yescharacteristic
316C23#1306331011yescharacteristic
317D4—3441no—
318D4—3441no—
319D4—3442no—
320D4—3442no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—862no—
334C2×C4—862no—
335C2×C4—862no—
336C2×C4—862no—
337C2×C4—3441no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1721no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4#1306328711yescharacteristic
348C2×C4C4×D17211yescharacteristic
349C2×C4#1306329811yescharacteristic
350C2×C4#1306330011yescharacteristic
351C8—81no—
352C8—3441no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—3444no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22#1458277711yescharacteristic
366C22#1458291412yes—
367C22#1458307312yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—3442no—
375C4—3441no—
376C4—1722no—
377C4—1722no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—6881no—
382C2#1913499711yescharacteristic
383C2#1913504211yescharacteristic
384C2#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#9414
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. #19137195C2semidirect
5. #19132924C2semidirect
6. #19132481C2semidirect
7. C43×#1297C2semidirect
11. #14582839C4semidirect
12. #14582817C4semidirect
192. #1297D43semidirect
219. C43#9414semidirect

Maximal subgroups

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

subgroupindex
#191400702
#191371952
#191331122
#191331102
#191329242
#191324812
C43×#12972
#941443