Finite Group Databasebeta

← #25081916

Subgroups — #25081916

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144713C211yesmaximal, characteristic, complemented
2#19144622C211yesmaximal, characteristic, complemented
3#19143675C211yesmaximal, characteristic, complemented
4#19134050C212yesmaximal, complemented
5#19134008C212yesmaximal, complemented
6#19133952C212yesmaximal, complemented
7#19133940C212yesmaximal, complemented
8#19133375C211yesmaximal, characteristic, complemented
9#19133300C211yesmaximal, characteristic, complemented
10#19133257C211yesmaximal, characteristic, complemented
11C43×#3207C211yesmaximal, characteristic
12C2×C4×Dic86C2211yescharacteristic
13#14583215—21no—
14#14583210—21no—
15#14583191C2212yes—
16#14583181C2212yes—
17#14583096C2212yes—
18#14583096C2212yes—
19#14583037—21no—
20#14583037—21no—
21C8×Dic86C2212yes—
22C8×Dic86C2212yes—
23#14583023—22no—
24#14582999—22no—
25C4×#10621883—22no—
26#14582956C2211yescharacteristic
27#14582952C2211yescharacteristic
28#14582952C2211yescharacteristic
29#14582949—22no—
30#14582652C2212yes—
31#14582650C2212yes—
32#14582648C2212yes—
33#14582645C2212yes—
34#14582643C2212yes—
35#14582643C2212yes—
36C43×#532C2211yescharacteristic
37C43×#532C2211yescharacteristic
38C43×#493C2211yescharacteristic
39C43×#492C2211yescharacteristic
40C43×#487C2211yescharacteristic
41C43×#486C2211yescharacteristic
42C43×#463—22no—
43C43×#449—22no—
44C43×#431C2211yescharacteristic
45C22×Dic86D411yescharacteristic
46C2×#10621883—22no—
47C2×#10621883—22no—
48C4×Dic86—21no—
49C4×Dic86—21no—
50C4×Dic86D412yes—
51C4×Dic86C2312yes—
52C2×C4⋊Dic43D411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×C4×Dic43—21no—
55#13063258—22no—
56#13063256—22no—
57C4⋊(C43⋊C8)C2312yes—
58C4⋊(C43⋊C8)C2312yes—
59C4⋊(C43⋊C8)C2312yes—
60Dic43⋊C8—22no—
61Dic43⋊C8—22no—
62#13063248—22no—
63#13063248—22no—
64#13063246—22no—
65#13063246—22no—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69#13063236—21no—
70C4×C43⋊C8—21no—
71C4×C43⋊C8—21no—
72C8×Dic43—22no—
73C8×Dic43—22no—
74C2×#41×C43—21no—
75C2×#41×C43—21no—
76C2×SD16×C43—22no—
77C2×D8×C43—22no—
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#127×C43C2311yescharacteristic
81#127×C43C2311yescharacteristic
82#124×C43—21no—
83#124×C43—21no—
84#121×C43—21no—
85#121×C43—21no—
86#121×C43—21no—
87#121×C43—21no—
88C4×D4×C43—21no—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C4⋊C8×C43D412yes—
94#103×C43—22no—
95#102×C43—22no—
96C22⋊C8×C43D412yes—
97C4×C8×C43C2311yescharacteristic
98C4×C8×C43C2311yescharacteristic
99#41×C43—82no—
100#41×C43—82no—
101C2×Q8×C43—21no—
102C2×Q8×C43—21no—
103C2×D4×C43—21no—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43—41no—
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×Dic43—21no—
117C22×Dic43—21no—
118C2×Dic86—21no—
119C2×Dic86—24no—
120C2×Dic86C2×D412yes—
121SD16×C43—82no—
122D8×C43—82no—
123C2×C8×C43C2×D412yes—
124C2×C8×C43C2×D412yes—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C22⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C42×C43C2×D411yescharacteristic
134C42×C43C2×D411yescharacteristic
135C42×C43#4111yescharacteristic
136C42×C43C2411yescharacteristic
137#10621883—44no—
138#10621883—44no—
139C4⋊Dic43—21no—
140C4⋊Dic43C2×D412yes—
141Dic43⋊C4—22no—
142Dic43⋊C4—22no—
143C4×Dic43—22no—
144C4×Dic43—22no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—22no—
147C2×C43⋊C8—22no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43#12111yescharacteristic
151Q8×C43—42no—
152Q8×C43—81no—
153D4×C43—42no—
154D4×C43—42no—
155D4×C43—42no—
156D4×C43—42no—
157D4×C43—81no—
158D4×C43—81no—
159D4×C43—82no—
160D4×C43—82no—
161C2×C4×C43—22no—
162C2×C4×C43—22no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—82no—
167C2×C4×C43—82no—
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43C22×D411yescharacteristic
172C2×C4×C43C22×D411yescharacteristic
173C2×C4×C43C2×#4111yescharacteristic
174C2×Dic43—24no—
175C2×Dic43—22no—
176C2×Dic43—22no—
177C2×Dic43—81no—
178Dic86—24no—
179Dic86—22no—
180Dic86#13514yes—
181C8×C43—22no—
182C8×C43—22no—
183C43⋊C8—42no—
184C43⋊C8—42no—
185C43⋊C8—42no—
186#19401—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43C2×#12111yescharacteristic
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—81no—
202C4×C43—81no—
203C4×C43C2×#13512yes—
204C4×C43#57712yes—
205Dic43—24no—
206Dic43—42no—
207#3207D4311yescharacteristic
208#3112—431no—
209#3103—431no—
210#2982—431no—
211#1684—432no—
212#1678—432no—
213#1668—432no—
214#1666—432no—
215#1572—431no—
216#1553—431no—
217#1543—431no—
218C2×C43—41no—
219C2×C43—161no—
220C2×C43—161no—
221C2×C43#304311yescharacteristic
222C2×C43#305011yescharacteristic
223C2×C43#306811yescharacteristic
224#532C2×D4311yescharacteristic
225#532C2×D4311yescharacteristic
226C2×C4×Q8—431no—
227#493C2×D4311yescharacteristic
228#492C2×D4311yescharacteristic
229#487C2×D4311yescharacteristic
230#486C2×D4311yescharacteristic
231#481—861no—
232#480—861no—
233#477—432no—
234#475—432no—
235#463—22no—
236#460—432no—
237#460—432no—
238#449—22no—
239#448—861no—
240#448—861no—
241C8×Q8—432no—
242C8×Q8—432no—
243C8×Q8—862no—
244#440—862no—
245C4×SD16—862no—
246#432—431no—
247#431—431no—
248#431—431no—
249#431—862no—
250#431C2×D4311yescharacteristic
251#335—432no—
252#334—432no—
253#333—432no—
254#332—432no—
255#331—432no—
256#331—432no—
257C43#1940111yescharacteristic, complemented, Sylow
258C2×#41—21no—
259C2×#41—21no—
260C22×Q8—431no—
261C2×SD16—22no—
262C2×SD16—862no—
263C2×SD16—862no—
264C2×D8—22no—
265C4⋊Q8C22×D4311yescharacteristic
266C4⋊Q8C22×D4311yescharacteristic
267#127C22×D4311yescharacteristic
268#127C22×D4311yescharacteristic
269#124—21no—
270#124—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275C4×Q8—432no—
276C4×Q8—432no—
277C4×Q8—861no—
278C4×Q8—861no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—431no—
284C2×C4⋊C4—861no—
285C2×C42—861no—
286C2×C42C22×D4311yescharacteristic
287#107—862no—
288#106—862no—
289C4⋊C8—432no—
290C4⋊C8—432no—
291C4⋊C8—432no—
292C4⋊C8—862no—
293C4⋊C8—862no—
294C4⋊C8C22⋊D4312yes—
295#103—22no—
296#103—862no—
297#103—862no—
298#102—22no—
299#102—862no—
300#102—862no—
301C22⋊C8—861no—
302C22⋊C8—861no—
303C22⋊C8—861no—
304C22⋊C8C22⋊D4312yes—
305#97—861no—
306C4×C8—862no—
307C4×C8—862no—
308C4×C8—861no—
309C4×C8—861no—
310C4×C8C22×D4311yescharacteristic
311C4×C8C22×D4311yescharacteristic
312#41—82no—
313#41—82no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—432no—
317C2×Q8—864no—
318C2×Q8—861no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C2×D4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190011yescharacteristic
333C22×C4C2×C22⋊D4311yescharacteristic
334SD16—82no—
335SD16—1724no—
336SD16—1724no—
337D8—82no—
338C2×C8—862no—
339C2×C8—862no—
340C2×C8—862no—
341C2×C8C2×C22⋊D4312yes—
342C2×C8C2×C22⋊D4312yes—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—432no—
348C4⋊C4—861no—
349C4⋊C4—862no—
350C4⋊C4—862no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—862no—
356C42—862no—
357C42D4×D4311yescharacteristic
358C42#1062190011yescharacteristic
359C42C2×C22⋊D4311yescharacteristic
360C42C23×D4311yescharacteristic
361C23—41no—
362C23—41no—
363C23#1306329611yescharacteristic
364Q8—42no—
365Q8—81no—
366Q8—434no—
367Q8—864no—
368Q8—862no—
369D4—42no—
370D4—42no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—82no—
376D4—82no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—864no—
385C2×C4—862no—
386C2×C4—862no—
387C2×C4—3441no—
388C2×C4#1306329611yescharacteristic
389C2×C4#1306329611yescharacteristic
390C2×C4#1306329611yescharacteristic
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4C22×C22⋊D4311yescharacteristic
393C2×C4C2×#1062190011yescharacteristic
394C8—22no—
395C8—22no—
396C8—1722no—
397C8—1722no—
398C8—1722no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22C2×#1306329611yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—81no—
414C4—81no—
415C4—864no—
416C4—1722no—
417C4#135×D4312yes—
418C4#1458371012yes—
419C2—41no—
420C2—161no—
421C2—161no—
422C2#1914411211yescharacteristic
423C2#1914417211yescharacteristic
424C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3207C2
socleC22×C43C2×#121
hypercenter#3207D43
hypocenterC43#19401
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3207

Complements

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

NH ≅ G/Ntype
1. #19144713C2semidirect
2. #19144622C2semidirect
3. #19143675C2semidirect
4. #19134050C2semidirect
5. #19134008C2semidirect
6. #19133952C2semidirect
7. #19133940C2semidirect
8. #19133375C2semidirect
9. #19133300C2semidirect
10. #19133257C2semidirect
257. C43#19401semidirect

Maximal subgroups

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

subgroupindex
#191447132
#191446222
#191436752
#191340502
#191340082
#191339522
#191339402
#191333752
#191333002
#191332572
C43×#32072
#1940143