Finite Group Databasebeta

← #25079787

Subgroups — #25079787

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145902C211yesmaximal, characteristic
2#19144920C211yesmaximal, characteristic, complemented
3#19143307C211yesmaximal, characteristic, complemented
4#19134144C212yesmaximal, complemented
5#19134130C212yesmaximal, complemented
6#19134048C212yesmaximal, complemented
7#19134034C212yesmaximal, complemented
8C2×#14582651C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10#19133270C211yesmaximal, characteristic, complemented
11C43×#3246C211yesmaximal, characteristic, complemented
12C2×#13063332—21no—
13#14583449C2211yescharacteristic
14#14583256—21no—
15#14583256—21no—
16#14583251C2211yescharacteristic
17#14583251C2211yescharacteristic
18#14583247C2211yescharacteristic
19#14583247C2211yescharacteristic
20#14583179C2212yes—
21#14583176—21no—
22#14583133—22no—
23#14583094C2212yes—
24#14583091—21no—
25#14582977—21no—
26#14582977C2212yes—
27D4×C43⋊C8—21no—
28D4×C43⋊C8C2212yes—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31#14582893—21no—
32#14582893—21no—
33#14582866—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582651C2212yes—
36#14582651C2212yes—
37#14582648C2212yes—
38#14582645C2212yes—
39#14582644C2212yes—
40#14582642C2212yes—
41C43×#533C2211yescharacteristic
42C43×#532C2211yescharacteristic
43C43×#476C2212yes—
44C43×#475—21no—
45C43×#465—22no—
46C43×#461C2212yes—
47C43×#460—21no—
48C2×C4⋊C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50C2×#10621882—22no—
51#13063332—44no—
52C2×#10621877—21no—
53C2×#10621877—22no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—22no—
56C22×C43⋊C8D411yescharacteristic
57C22×C43⋊C8D411yescharacteristic
58#13063325C2311yescharacteristic
59#13063322C2311yescharacteristic
60#13063313—21no—
61#13063299—21no—
62#13063299—21no—
63C4×D172—21no—
64C4×D172—21no—
65#13063258—22no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)C2312yes—
69C4⋊(C43⋊C8)C2312yes—
70#13063248—21no—
71#13063248—21no—
72#13063248—21no—
73#13063248—21no—
74#13063246—22no—
75#13063245—22no—
76#13063245—21no—
77#13063245—21no—
78#13063245—21no—
79#13063245—21no—
80C22⋊(C43⋊C8)—22no—
81C22⋊(C43⋊C8)—22no—
82C4×C43⋊C8D411yescharacteristic
83C4×C43⋊C8D411yescharacteristic
84C4×C43⋊C8C2311yescharacteristic
85C4×C43⋊C8C2311yescharacteristic
86C2×#41×C43—21no—
87C2×SD16×C43—22no—
88C22×C8×C43—21no—
89C4⋊Q8×C43D411yescharacteristic
90C4⋊Q8×C43C2311yescharacteristic
91C4⋊Q8×C43C2311yescharacteristic
92#127×C43D411yescharacteristic
93#125×C43—21no—
94#124×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97#121×C43—21no—
98#121×C43D412yes—
99C4×Q8×C43—21no—
100C4×Q8×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43C2312yes—
103#117×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#106×C43—22no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43C2312yes—
108#103×C43—22no—
109#102×C43—22no—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—22no—
118C2×D4×C43C2×D412yes—
119C22×C4×C43—22no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C2×C22⋊D43—41no—
124#10621898—42no—
125#10621898—42no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×C4×D43—41no—
130C2×Dic86—21no—
131SD16×C43—82no—
132C2×C8×C43—22no—
133C2×C8×C43—81no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43C2×D412yes—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C42×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43#4111yescharacteristic
149C42×C43C2411yescharacteristic
150#10621882—82no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153C4⋊Dic43—21no—
154C4⋊Dic43—21no—
155#10621877—44no—
156#10621877—42no—
157C2×C43⋊C8—22no—
158C2×C43⋊C8—22no—
159C2×C43⋊C8—22no—
160C2×C43⋊C8—22no—
161C2×C43⋊C8—44no—
162C2×C43⋊C8—81no—
163C2×C43⋊C8C2×D411yescharacteristic
164C2×C43⋊C8C2×D411yescharacteristic
165C2×C43⋊C8C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167C23×C43—22no—
168C23×C43#12111yescharacteristic
169C22×D43—41no—
170Q8×C43—42no—
171Q8×C43—41no—
172Q8×C43—41no—
173Q8×C43—81no—
174D4×C43—22no—
175D4×C43—22no—
176D4×C43—42no—
177D4×C43—44no—
178D4×C43—42no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—22no—
182C2×C4×C43—41no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#13512yes—
191C2×C4×C43AGL(1,ℤ/8)12yes—
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C22⋊D43—82no—
196C2×Dic43—41no—
197D172—41no—
198D172—41no—
199D172—41no—
200D172—41no—
201D172—81no—
202C4×D43—82no—
203Dic86—41no—
204Dic86—41no—
205C8×C43—42no—
206C43⋊C8—21no—
207C43⋊C8—21no—
208C43⋊C8—21no—
209C43⋊C8—21no—
210C43⋊C8—42no—
211C43⋊C8—42no—
212#19201—431nomaximal, Sylow
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—42no—
216C22×C43—42no—
217C22×C43—42no—
218C22×C43#46312yes—
219C22×C43C2×#12111yescharacteristic
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—81no—
228C4×C43—81no—
229C4×C43#46312yes—
230C4×C43C2×#13511yescharacteristic
231C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C43#57611yescharacteristic
233C4×C43#57811yescharacteristic
234Dic43—81no—
235#3246D4311yescharacteristic, complemented
236#3245—431no—
237#3131—431no—
238#2931—431no—
239#1699—432no—
240#1697—432no—
241#1683—432no—
242#1681—432no—
243C2×#335—431no—
244#1550—431no—
245#1547—431no—
246C2×C43—22no—
247C2×C43—82no—
248C2×C43C2×#46311yescharacteristic
249C2×C43#306111yescharacteristic
250C2×C43#306711yescharacteristic
251D43—161no—
252C2×#131—861no—
253#533C2×D4311yescharacteristic
254#532—431no—
255#532C2×D4311yescharacteristic
256#488—861no—
257#488—861no—
258#487—431no—
259#487—431no—
260#486—431no—
261#486—431no—
262#476C2×D4312yes—
263#475—21no—
264#474—432no—
265#474—861no—
266#466—862no—
267#465—22no—
268#461C2×D4312yes—
269#460—21no—
270#459—432no—
271#459—861no—
272#436—432no—
273#436—861no—
274C8×D4—432no—
275C8×D4—861no—
276#423—431no—
277C2×C4⋊C8—431no—
278C2×C4⋊C8C2×D4311yescharacteristic
279#416—861no—
280#416—861no—
281#408—861no—
282C2×C4×C8—431no—
283#335—432no—
284#335—432no—
285#333—432no—
286#332—432no—
287#332—432no—
288#331—432no—
289C43#1920111yescharacteristic, complemented, Sylow
290C2×#41—21no—
291C2×#41—861no—
292C2×SD16—22no—
293C2×D8—862no—
294#131—1724no—
295C2×M16—862no—
296C2×M16—861no—
297C22×C8—21no—
298C22×C8—431no—
299C22×C8—431no—
300C22×C8—862no—
301C22×C8—861no—
302C4⋊Q8—431no—
303C4⋊Q8C22⋊D4311yescharacteristic
304C4⋊Q8C22×D4311yescharacteristic
305C4⋊Q8C22×D4311yescharacteristic
306#127—431no—
307#127C22⋊D4311yescharacteristic
308#125—21no—
309#124—21no—
310#124—861no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313#121—21no—
314#121—861no—
315#121—861no—
316#121C22⋊D4312yes—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×D4—21no—
320C4×D4—861no—
321C4×D4—861no—
322C4×D4C22×D4312yes—
323#117—21no—
324C2×C42C22×D4311yescharacteristic
325#107—862no—
326#106—22no—
327C4⋊C8—21no—
328C4⋊C8—432no—
329C4⋊C8—432no—
330C4⋊C8—861no—
331C4⋊C8—861no—
332C4⋊C8C22×D4312yes—
333#103—22no—
334#103—861no—
335#103—861no—
336#103—861no—
337#103—861no—
338#102—22no—
339#102—861no—
340#102—861no—
341#102—861no—
342#102—861no—
343#102—862no—
344#102—862no—
345C22⋊C8—862no—
346C22⋊C8—862no—
347C4×C8—431no—
348C4×C8—431no—
349C4×C8—431no—
350C4×C8—431no—
351#41—42no—
352#41—42no—
353#41—1722no—
354#41—1722no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—861no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—861no—
363C2×D4—861no—
364C2×D4—861no—
365C2×D4—1721no—
366C2×D4C2×C22⋊D4312yes—
367C22×C4—22no—
368C22×C4—1721no—
369C22×C4D4×D4311yescharacteristic
370C22×C4#1062190011yescharacteristic
371C22×C4C2×C22⋊D4311yescharacteristic
372SD16—82no—
373D8—3442no—
374M16—1724no—
375M16—1722no—
376C2×C8—22no—
377C2×C8—81no—
378C2×C8—431no—
379C2×C8—431no—
380C2×C8—431no—
381C2×C8—431no—
382C2×C8—862no—
383C2×C8—862no—
384C2×C8—862no—
385C2×C8—862no—
386C2×C8—3441no—
387C2×C8—1724no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—861no—
396C4⋊C4—861no—
397C4⋊C4C2×C22⋊D4312yes—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—41no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C42—41no—
404C42D4×D4311yescharacteristic
405C42#1062190011yescharacteristic
406C42C2×C22⋊D4311yescharacteristic
407C42C23×D4311yescharacteristic
408C23—22no—
409C23—1721no—
410C23#1306329711yescharacteristic
411Q8—42no—
412Q8—41no—
413Q8—41no—
414Q8—81no—
415Q8—1721no—
416Q8—1721no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—44no—
421D4—42no—
422D4—3441no—
423D4—3442no—
424D4—1721no—
425D4—1721no—
426D4—1721no—
427D4—1721no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—3442no—
437C2×C4—1721no—
438C2×C4#1306329711yescharacteristic
439C2×C4#1306329711yescharacteristic
440C2×C4#1306329711yescharacteristic
441C2×C4#1306334612yes—
442C2×C4#1306335212yes—
443C2×C4C2×D4×D4311yescharacteristic
444C2×C4C22×C22⋊D4311yescharacteristic
445C2×C4C2×#1062190011yescharacteristic
446C8—42no—
447C8—861no—
448C8—861no—
449C8—861no—
450C8—861no—
451C8—1722no—
452C8—1722no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—3441no—
459C22—3441no—
460C22—3441no—
461C22#1458311612yes—
462C22C2×#1306329711yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—3441no—
470C4#1458311612yes—
471C4C2×#1306334611yescharacteristic
472C4C2×#1306335211yescharacteristic
473C4#1458370211yescharacteristic
474C4#1458371411yescharacteristic
475C2—22no—
476C2—82no—
477C2—6881no—
478C2C2×#1458311611yescharacteristic
479C2#1914426211yescharacteristic
480C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3246C2
socleC22×C43C2×#121
prime radical#19145902C2
hypercenter#3246D43
hypocenterC43#19201
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
2. #19144920C2semidirect
3. #19143307C2semidirect
4. #19134144C2semidirect
5. #19134130C2semidirect
6. #19134048C2semidirect
7. #19134034C2semidirect
8. C2×#14582651C2semidirect
9. #19133285C2semidirect
10. #19133270C2semidirect
11. C43×#3246C2semidirect
235. #3246D43semidirect
289. C43#19201semidirect

Maximal subgroups

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

subgroupindex
#191459022
#191449202
#191433072
#191341442
#191341302
#191340482
#191340342
C2×#145826512
#191332852
#191332702
C43×#32462
#1920143