Finite Group Databasebeta

← #25081923

Subgroups — #25081923

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#19145524C211yesmaximal, characteristic
2#19144626C211yesmaximal, characteristic, complemented
3#19143676C211yesmaximal, characteristic, complemented
4#19134055C212yesmaximal, complemented
5#19134013C212yesmaximal, complemented
6#19133953C212yesmaximal, complemented
7#19133941C212yesmaximal, complemented
8#19133376C211yesmaximal, characteristic, complemented
9#19133301C211yesmaximal, characteristic, complemented
10#19133257C211yesmaximal, characteristic, complemented
11C43×#3112C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13#14583275C2211yescharacteristic
14#14583271C2211yescharacteristic
15#14583251C2211yescharacteristic
16#14583247C2211yescharacteristic
17#14583217—21no—
18#14583184C2212yes—
19#14583114—22no—
20#14583099C2212yes—
21#14583042—22no—
22#14583038—21no—
23Q8×C43⋊C8—22no—
24Q8×C43⋊C8C2212yes—
25Q8×C43⋊C8C2212yes—
26C4×#10621884—22no—
27#14582952—22no—
28#14582952C2211yescharacteristic
29#14582952C2211yescharacteristic
30#14582952C2211yescharacteristic
31#14582651C2212yes—
32#14582649C2212yes—
33#14582648C2212yes—
34#14582644C2212yes—
35#14582643C2212yes—
36#14582642C2212yes—
37C43×#532C2211yescharacteristic
38C2×C4×Q8×C43C2211yescharacteristic
39C43×#480—21no—
40C43×#477C2212yes—
41C43×#460C2212yes—
42C43×#448—21no—
43C43×#440—22no—
44C43×#432C2211yescharacteristic
45C2×#10621898—21no—
46C2×#10621883—22no—
47C2×#10621884—22no—
48C2×#10621882—22no—
49#13063325C2311yescharacteristic
50#13063322C2311yescharacteristic
51#13063313—21no—
52#13063299—21no—
53#13063299—21no—
54C4×D172—21no—
55C4×D172—21no—
56#13063256—22no—
57C4⋊(C43⋊C8)—22no—
58C4⋊(C43⋊C8)—22no—
59C4⋊(C43⋊C8)D412yes—
60C4⋊(C43⋊C8)C2312yes—
61C4⋊(C43⋊C8)C2312yes—
62#13063249—22no—
63#13063248—22no—
64#13063245—22no—
65#13063245—22no—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)D412yes—
69C4×C43⋊C8—21no—
70C4×C43⋊C8—21no—
71C4×C43⋊C8—22no—
72C4×C43⋊C8—22no—
73C4×C43⋊C8C2311yescharacteristic
74C4×C43⋊C8C2311yescharacteristic
75C2×#41×C43—21no—
76C22×Q8×C43D411yescharacteristic
77C2×SD16×C43—22no—
78C4⋊Q8×C43C2311yescharacteristic
79#127×C43C2311yescharacteristic
80#124×C43—21no—
81#121×C43—21no—
82#121×C43—21no—
83C4×Q8×C43—21no—
84C4×Q8×C43—21no—
85C4×Q8×C43D412yes—
86C4×Q8×C43C2312yes—
87C4×D4×C43—21no—
88C4×D4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C42×C43—21no—
92C2×C42×C43C2311yescharacteristic
93#107×C43—22no—
94C4⋊C8×C43C2312yes—
95#103×C43—22no—
96#102×C43—22no—
97C22⋊C8×C43—21no—
98#97×C43—21no—
99#41×C43—82no—
100C2×Q8×C43—24no—
101C2×Q8×C43—21no—
102C2×Q8×C43—21no—
103C2×Q8×C43C2×D412yes—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—41no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—41no—
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C2×C22⋊D43—41no—
115#10621898—82no—
116C2×D172—21no—
117C2×D172—21no—
118C2×D172—21no—
119C2×C4×D43—41no—
120C2×Dic86—21no—
121SD16×C43—44no—
122C2×C8×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43C2×D412yes—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C42×C43—22no—
132C42×C43—22no—
133C42×C43C2×D411yescharacteristic
134C42×C43C2×D411yescharacteristic
135C42×C43#4111yescharacteristic
136C42×C43C2411yescharacteristic
137#10621884—44no—
138#10621883—82no—
139#10621882—82no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8C2×D412yes—
147C2×C43⋊C8C2×D412yes—
148C23×C43—41no—
149C23×C43#12111yescharacteristic
150C22×D43—41no—
151Q8×C43—24no—
152Q8×C43—22no—
153Q8×C43—81no—
154Q8×C43#13514yes—
155D4×C43—42no—
156D4×C43—42no—
157D4×C43—81no—
158D4×C43—82no—
159C2×C4×C43—24no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43—22no—
163C2×C4×C43—22no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—82no—
167C2×C4×C43—81no—
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43C22×D411yescharacteristic
172C2×C4×C43C22×D411yescharacteristic
173C2×C4×C43C2×#4111yescharacteristic
174C22⋊D43—82no—
175C2×Dic43—41no—
176D172—42no—
177D172—42no—
178D172—81no—
179C4×D43—82no—
180Dic86—42no—
181C8×C43—42no—
182C43⋊C8—22no—
183C43⋊C8—22no—
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×C43C2×#12111yescharacteristic
194C2×D43—81no—
195C2×D43—81no—
196C2×D43—81no—
197C4×C43—21no—
198C4×C43—24no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—42no—
203C4×C43—81no—
204C4×C43C2×#13512yes—
205C4×C43#57712yes—
206Dic43—81no—
207#3207—431no—
208#3112D4311yescharacteristic, complemented
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#304311yescharacteristic
221C2×C43#305011yescharacteristic
222C2×C43#306811yescharacteristic
223D43—161no—
224#532—431no—
225#532C2×D4311yescharacteristic
226C2×C4×Q8C2×D4311yescharacteristic
227#493—431no—
228#492—431no—
229#487—431no—
230#486—431no—
231#481—861no—
232#480—21no—
233#477C2×D4312yes—
234#475—432no—
235#463—862no—
236#460—432no—
237#460C2×D4312yes—
238#449—862no—
239#448—21no—
240#448—861no—
241C8×Q8—432no—
242C8×Q8—432no—
243C8×Q8—862no—
244#440—22no—
245C4×SD16—862no—
246#432C2×D4311yescharacteristic
247#431—431no—
248#431—431no—
249#431—431no—
250#431—862no—
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—861no—
260C22×Q8C22⋊D4311yescharacteristic
261C2×SD16—22no—
262C2×SD16—862no—
263C2×SD16—862no—
264C2×D8—862no—
265C4⋊Q8—431no—
266C4⋊Q8C22×D4311yescharacteristic
267#127—431no—
268#127C22×D4311yescharacteristic
269#124—21no—
270#124—861no—
271#121—21no—
272#121—21no—
273#121—861no—
274#121—861no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×Q8C22⋊D4312yes—
278C4×Q8C22×D4312yes—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—861no—
282C4×D4—861no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4C22⋊D4311yescharacteristic
285C2×C42—21no—
286C2×C42C22×D4311yescharacteristic
287#107—22no—
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—21no—
302C22⋊C8—432no—
303C22⋊C8—861no—
304C22⋊C8—861no—
305#97—21no—
306C4×C8—431no—
307C4×C8—431no—
308C4×C8—862no—
309C4×C8—862no—
310C4×C8—861no—
311C4×C8—861no—
312#41—82no—
313#41—3442no—
314C2×Q8—24no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—861no—
318C2×Q8C2×C22⋊D4312yes—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—1721no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—1721no—
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190011yescharacteristic
333C22×C4C2×C22⋊D4311yescharacteristic
334SD16—44no—
335SD16—3442no—
336SD16—1724no—
337D8—3442no—
338C2×C8—22no—
339C2×C8—432no—
340C2×C8—432no—
341C2×C8—862no—
342C2×C8—862no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4C2×C22⋊D4312yes—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C42—22no—
356C42—22no—
357C42D4×D4311yescharacteristic
358C42#1062190011yescharacteristic
359C42C2×C22⋊D4311yescharacteristic
360C42C23×D4311yescharacteristic
361C23—41no—
362C23—1721no—
363C23#1306329711yescharacteristic
364Q8—24no—
365Q8—22no—
366Q8—81no—
367Q8—1722no—
368Q8#1306334514yes—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—82no—
373D4—3441no—
374D4—3442no—
375D4—1722no—
376D4—1722no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—82no—
385C2×C4—81no—
386C2×C4—3442no—
387C2×C4—1721no—
388C2×C4#1306329711yescharacteristic
389C2×C4#1306329711yescharacteristic
390C2×C4#1306329711yescharacteristic
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4C22×C22⋊D4311yescharacteristic
393C2×C4C2×#1062190011yescharacteristic
394C8—42no—
395C8—862no—
396C8—862no—
397C8—1722no—
398C8—1722no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—3441no—
406C22—3441no—
407C22—3441no—
408C22C2×#1306329711yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—24no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—3441no—
417C4C2×#1306334512yes—
418C4#1458370812yes—
419C2—41no—
420C2—161no—
421C2—6881no—
422C2#1914411811yescharacteristic
423C2#1914417311yescharacteristic
424C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3112C2
socleC22×C43C2×#121
prime radical#19145524C2
hypercenter#3112D43
hypocenterC43#19401
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3112

Complements

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

NH ≅ G/Ntype
2. #19144626C2semidirect
3. #19143676C2semidirect
4. #19134055C2semidirect
5. #19134013C2semidirect
6. #19133953C2semidirect
7. #19133941C2semidirect
8. #19133376C2semidirect
9. #19133301C2semidirect
10. #19133257C2semidirect
11. C43×#3112C2semidirect
208. #3112D43semidirect
257. C43#19401semidirect

Maximal subgroups

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

subgroupindex
#191455242
#191446262
#191436762
#191340552
#191340132
#191339532
#191339412
#191333762
#191333012
#191332572
C43×#31122
#1940143