Finite Group Databasebeta

← #24993331

Subgroups — #24993331

Order 11008.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145716C211yesmaximal, characteristic
2#19135427C211yesmaximal, characteristic
3#19133267C211yesmaximal, characteristic, complemented
4#19133154C211yesmaximal, characteristic
5#19132453C211yesmaximal, characteristic, complemented
6#19132424C211yesmaximal, characteristic, complemented
7C43×#2327C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583302C412yescomplemented
10#14583247C412yescomplemented
11#14583212—22no—
12#14583176—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C2×#13063253—21no—
17C2×#13063253—21no—
18#14582645—22no—
19#14582632—22no—
20C2×C4⋊Q8×C43C2211yescharacteristic
21C2×C4×Q8×C43—21no—
22C43×#391—21no—
23C43×#387—22no—
24C43×#387—22no—
25C43×#382C2211yescharacteristic
26C43×#376C2211yescharacteristic
27C2×#10621898—21no—
28C2×#10621877—21no—
29#13063325C2×C411yescharacteristic
30#13063322C2×C411yescharacteristic
31#13063313—21no—
32#13063299—21no—
33#13063299—21no—
34C4×D172—21no—
35C4×D172—21no—
36#13063258—24no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41#13063253—42no—
42#13063253—42no—
43#13063245—24no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8C2×C412yes—
48C22×Q8×C43—21no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43C2×C412yes—
52C4⋊Q8×C43D412yes—
53C4×Q8×C43—42no—
54C4×Q8×C43—42no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—22no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43D412yes—
59C2×C42×C43—22no—
60C2×C42×C43D411yescharacteristic
61C2×C42×C43D411yescharacteristic
62C2×C42×C43C2311yescharacteristic
63#95×C43—24no—
64#95×C43—21no—
65#95×C43—21no—
66#95×C43—21no—
67#95×C43D412yes—
68C2×Q8×C43—22no—
69C2×Q8×C43—22no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C22×C4×C43—21no—
75C22×C4×C43—22no—
76C22×C4×C43—21no—
77C22×C4×C43—22no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C2×C22⋊D43—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—21no—
89C2×C4×D43—41no—
90C2×Dic86—21no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—44no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43C22⋊C414yes—
98C42×C43—21no—
99C42×C43—21no—
100C42×C43—21no—
101C42×C43—44no—
102C42×C43D812yes—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C42×C43#4111yescharacteristic
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111#10621877—41no—
112#10621877—41no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C23×C43#12011yescharacteristic
117C22×D43—41no—
118Q8×C43—42no—
119Q8×C43—42no—
120Q8×C43—42no—
121Q8×C43—42no—
122C2×C4×C43—24no—
123C2×C4×C43—22no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12311yescharacteristic
142C2×C4×C43C2×D811yescharacteristic
143C2×C4×C43#13511yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C22⋊D43—81no—
147C22⋊D43—81no—
148C2×Dic43—41no—
149D172—42no—
150D172—41no—
151D172—41no—
152D172—81no—
153C4×D43—81no—
154C4×D43—81no—
155Dic86—41no—
156Dic86—41no—
157C43⋊C8—42no—
158C43⋊C8—81no—
159C43⋊C8—81no—
160#9300—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43#38611yescharacteristic
164C22×C43#44711yescharacteristic
165C22×C43#44911yescharacteristic
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—42no—
174C4×C43—44no—
175C4×C43—82no—
176C4×C43—81no—
177C4×C43C4×D811yescharacteristic
178C4×C43#44211yescharacteristic
179C4×C43#45911yescharacteristic
180C4×C43#46311yescharacteristic
181Dic43—81no—
182#3226—431no—
183#2327D4311yescharacteristic, complemented
184#1963—431no—
185#1546—431no—
186#1517—431no—
187#1286—431no—
188#1274—431no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43#187911yescharacteristic
192C2×C43#190511yescharacteristic
193C2×C43#191211yescharacteristic
194D43—161no—
195#532—431no—
196C2×C4⋊Q8C2×D4311yescharacteristic
197C2×C4×Q8—21no—
198#500—432no—
199#486—432no—
200#480—862no—
201#474—862no—
202#431—431no—
203#431—431no—
204#423—431no—
205C2×#104—861no—
206C2×#104—861no—
207#391—21no—
208#387—22no—
209#387—22no—
210#382C2×D4311yescharacteristic
211#376C2×D4311yescharacteristic
212#332—862no—
213#327—862no—
214C43#930011yescharacteristic, complemented, Sylow
215C2×#41—861no—
216C22×Q8—21no—
217C2×M16—861no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—431no—
221C4⋊Q8C4×D4312yes—
222C4⋊Q8D17212yes—
223#127—431no—
224#124—861no—
225#121—861no—
226#121—861no—
227C4×Q8—42no—
228C4×Q8—42no—
229C4×D4—861no—
230C4×D4—861no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C22⋊D4312yes—
235C2×C42—22no—
236C2×C42C22⋊D4311yescharacteristic
237C2×C42C22⋊D4311yescharacteristic
238C2×C42C22×D4311yescharacteristic
239#107—864no—
240C4⋊C8—861no—
241C4⋊C8—861no—
242C4⋊C8—861no—
243C4⋊C8—861no—
244#104—1722no—
245#104—1722no—
246#102—864no—
247C22⋊C8—861no—
248C22⋊C8—861no—
249C4×C8—432no—
250C4×C8—861no—
251#95—24no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95C22⋊D4312yes—
256#41—1721no—
257#41—1721no—
258#41—1721no—
259#41—1721no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—1721no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—1721no—
276C22×C4C2×C22⋊D4311yescharacteristic
277C22×C4C2×C22⋊D4311yescharacteristic
278C22×C4C2×C22⋊D4311yescharacteristic
279M16—1721no—
280M16—1721no—
281C2×C8—862no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—44no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4(C2×D43)⋊C414yes—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—44no—
299C42#1062188212yes—
300C42C2×C4×D4311yescharacteristic
301C42C2×D17211yescharacteristic
302C42#1062189811yescharacteristic
303C42#1062189811yescharacteristic
304C23—1721no—
305C23#1306329411yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—42no—
309Q8—42no—
310Q8—1721no—
311Q8—1721no—
312D4—3441no—
313D4—3441no—
314D4—3441no—
315D4—1722no—
316D4—1721no—
317D4—1721no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—1721no—
335C2×C4C2×(C2×D43)⋊C411yescharacteristic
336C2×C4C4×C22⋊D4311yescharacteristic
337C2×C4C4×C22⋊D4311yescharacteristic
338C2×C4#1306329911yescharacteristic
339C2×C4#1306329911yescharacteristic
340C2×C4#1306330811yescharacteristic
341C2×C4C2×#1062188211yescharacteristic
342C2×C4#1306334511yescharacteristic
343C2×C4#1306335011yescharacteristic
344C2×C4#1306335111yescharacteristic
345C8—3441no—
346C8—3441no—
347C8—1722no—
348C22—21no—
349C22—21no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22#1458277811yescharacteristic
354C22#1458303311yescharacteristic
355C22#1458304411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—3441no—
365C4C4×#1062188211yescharacteristic
366C4#1458300911yescharacteristic
367C4#1458309411yescharacteristic
368C4#1458311411yescharacteristic
369C2—21no—
370C2—21no—
371C2—6881no—
372C2#1913494311yescharacteristic
373C2#1913508911yescharacteristic
374C2#1913513211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2327C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2327D43
hypocenterC43#9300
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
3. #19133267C2semidirect
5. #19132453C2semidirect
6. #19132424C2semidirect
7. C43×#2327C2semidirect
9. #14583302C4semidirect
10. #14583247C4semidirect
183. #2327D43semidirect
214. C43#9300semidirect

Maximal subgroups

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

subgroupindex
#191457162
#191354272
#191332672
#191331542
#191324532
#191324242
C43×#23272
#930043