Finite Group Databasebeta

← #24994064

Subgroups — #24994064

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#19140076C211yesmaximal, characteristic
2#19137195C211yesmaximal, characteristic, complemented
3#19133111C211yesmaximal, characteristic
4#19132924C211yesmaximal, characteristic, complemented
5#19132481C211yesmaximal, characteristic, complemented
6#19132480C211yesmaximal, characteristic, complemented
7C43×#1507C211yesmaximal, characteristic
8C22×Dic43⋊C4C2211yescharacteristic
9#14582863C2211yescharacteristic
10#14582837C412yescomplemented
11#14582813C412yescomplemented
12#14582793—22no—
13#14582783—22no—
14#14582781—22no—
15#14582779—21no—
16#14582779—21no—
17#14582760—21no—
18#14582757—21no—
19C4×C22⋊Dic43C2211yescharacteristic
20C4×C22⋊Dic43C2211yescharacteristic
21#14582633—22no—
22#14582624—22no—
23C2×#121×C43C2211yescharacteristic
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C43×#327—22no—
27C23×Dic43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C2×#10621877—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—22no—
35C2×Dic43⋊C4C2×C412yes—
36C2×Dic43⋊C4D412yes—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—22no—
40C2×C22⋊Dic43—22no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43—21no—
43C22⋊(C43⋊C8)—21no—
44C22⋊(C43⋊C8)—21no—
45C43⋊#95—22no—
46C43⋊#95—24no—
47C43⋊#95—22no—
48C43⋊#95—22no—
49C43⋊#95C2×C412yes—
50C43⋊#95D412yes—
51C22×D4×C43—21no—
52C22×D4×C43C2×C411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C2×M16×C43—21no—
55#121×C43—21no—
56#121×C43—21no—
57#121×C43—21no—
58#121×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C42×C43—21no—
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65#95×C43D412yes—
66C24×C43—21no—
67C24×C43C2×D411yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—44no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—81no—
74C22×C4×C43—21no—
75C22×C4×C43—22no—
76C22×C4×C43—81no—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×Dic43—22no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—42no—
90C22×Dic43—81no—
91C22×Dic43C22⋊C412yes—
92C22×Dic43C22⋊C412yes—
93M16×C43—81no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C42×C43—81no—
101C22⋊Dic43—42no—
102C22⋊Dic43—42no—
103C22⋊Dic43—44no—
104C22⋊Dic43—82no—
105Dic43⋊C4—22no—
106Dic43⋊C4—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—22no—
109Dic43⋊C4—82no—
110C4×Dic43—81no—
111C4×Dic43—81no—
112#10621877—81no—
113C2×C43⋊C8—41no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—41no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—41no—
120C23×C43—42no—
121C23×C43C2×C22⋊C411yescharacteristic
122C23×C43#12011yescharacteristic
123C23×C43#12311yescharacteristic
124D4×C43—81no—
125D4×C43—81no—
126D4×C43—82no—
127D4×C43—82no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—22no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—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—84no—
170C22×C43—81no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43#38611yescharacteristic
174C22×C43#42112yes—
175C22×C43#45412yes—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—82no—
181C4×C43—81no—
182Dic43—42no—
183Dic43—42no—
184Dic43—82no—
185Dic43—82no—
186#2591—431no—
187#2313—431no—
188#1507—431no—
189#1507D4311yescharacteristic
190#1463—431no—
191#1297—431no—
192#1297—431no—
193C2×C43—22no—
194C2×C43—22no—
195C2×C43—41no—
196C2×C43—161no—
197C2×C43#188811yescharacteristic
198C2×C43#189711yescharacteristic
199C2×C43#191311yescharacteristic
200C2×#121C2×D4311yescharacteristic
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⋊C4—431no—
215C4×C22⋊C4C2×D4311yescharacteristic
216#327—22no—
217#327—862no—
218#324—862no—
219C43#941411yescharacteristic, complemented, Sylow
220C22×D4—21no—
221C22×D4C4×D4311yescharacteristic
222C23×C4—431no—
223C23×C4—431no—
224C23×C4C22×D4311yescharacteristic
225C2×M16—21no—
226C2×M16—861no—
227#121—21no—
228#121—21no—
229#121—21no—
230#121—21no—
231C2×C4⋊C4—432no—
232C2×C4⋊C4—432no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—862no—
238C2×C4⋊C4C4×D4311yescharacteristic
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—861no—
247C2×C42—861no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—861no—
251C22⋊C8—861no—
252#95—432no—
253#95—432no—
254#95—862no—
255#95—862no—
256#95—862no—
257#95—864no—
258#95C22⋊D4312yes—
259C24—21no—
260C24D4×D4311yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—81no—
267C22×C4—21no—
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—862no—
277C22×C4—862no—
278C22×C4—3441no—
279C22×C4—1722no—
280C22×C4C2×C4×D4311yescharacteristic
281C22×C4#1062189811yescharacteristic
282C22×C4D4×D4311yescharacteristic
283C22×C4D4×D4311yescharacteristic
284C22×C4#1062190011yescharacteristic
285C22×C4C2×C22⋊D4311yescharacteristic
286M16—81no—
287M16—3441no—
288C2×C8—41no—
289C2×C8—1721no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—862no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C4⋊C4—862no—
296C4⋊C4—3442no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—3442no—
301C22⋊C4—1724no—
302C22⋊C4—1722no—
303C22⋊C4—1722no—
304C42—81no—
305C42—3441no—
306C42—3441no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23C22⋊C4×D4311yescharacteristic
315C23#1306329311yescharacteristic
316C23#1306330711yescharacteristic
317D4—81no—
318D4—81no—
319D4—82no—
320D4—82no—
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—41no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—862no—
335C2×C4—862no—
336C2×C4—3441no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4(C22⋊D43)⋊C411yescharacteristic
348C2×C4C4×C22⋊D4311yescharacteristic
349C2×C4#1306329611yescharacteristic
350C2×C4#1306329811yescharacteristic
351C8—81no—
352C8—3441no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—84no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22#1458277511yescharacteristic
366C22#1458291412yes—
367C22#1458307012yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—81no—
374C4—3442no—
375C4—3442no—
376C4—1722no—
377C4—1722no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2#1913499511yescharacteristic
383C2#1913504011yescharacteristic
384C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1507C2
socleC22×C43#386
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenter#1507D43
hypocenterC43#9414
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #19137195C2semidirect
4. #19132924C2semidirect
5. #19132481C2semidirect
6. #19132480C2semidirect
10. #14582837C4semidirect
11. #14582813C4semidirect
219. C43#9414semidirect

Maximal subgroups

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

subgroupindex
#191400762
#191371952
#191331112
#191329242
#191324812
#191324802
C43×#15072
#941443