Finite Group Databasebeta

← #25080437

Subgroups — #25080437

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic
2#19144067C211yesmaximal, characteristic, complemented
3C2×Q8×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134041C212yesmaximal, complemented
5#19134037C212yesmaximal, complemented
6#19133987C212yesmaximal, complemented
7#19133953C212yesmaximal, complemented
8#19133353C211yesmaximal, characteristic, complemented
9#19133273C211yesmaximal, characteristic, complemented
10#19133272C211yesmaximal, characteristic, complemented
11C43×#3037C211yesmaximal, characteristic, complemented
12C2×#13063356—21no—
13#14583449C2211yescharacteristic
14#14583302C2211yescharacteristic
15#14583275C2211yescharacteristic
16#14583247C2211yescharacteristic
17#14583245C2211yescharacteristic
18#14583133—21no—
19#14583133—21no—
20#14583121—22no—
21#14583109C2212yes—
22#14583099C2212yes—
23Q8×C43⋊C8—21no—
24Q8×C43⋊C8—21no—
25Q8×C43⋊C8C2212yes—
26Q8×C43⋊C8C2212yes—
27C4×#10621882—21no—
28C4×#10621882—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)—21no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32#14582898—21no—
33C2×C4×C43⋊C8—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582651C2212yes—
36#14582651C2212yes—
37#14582646C2212yes—
38#14582645C2212yes—
39#14582643C2212yes—
40#14582642C2212yes—
41C2×#137×C43—21no—
42C43×#532C2211yescharacteristic
43C2×C4×Q8×C43C2211yescharacteristic
44C43×#464—22no—
45C43×#462C2212yes—
46C43×#460C2212yes—
47C43×#423C2211yescharacteristic
48C43×#417—21no—
49C2×#10621898—21no—
50#13063356—44no—
51C2×#10621885—22no—
52C2×#10621884—22no—
53C2×#10621882—21no—
54C2×#10621882—21no—
55C2×#10621877—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8D411yescharacteristic
58C22×C43⋊C8D411yescharacteristic
59#13063325C2311yescharacteristic
60#13063322C2311yescharacteristic
61#13063313—21no—
62#13063299—21no—
63#13063299—21no—
64C4×D172—21no—
65C4×D172—21no—
66#13063258—21no—
67#13063258—21no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)—22no—
71C4⋊(C43⋊C8)—22no—
72C4⋊(C43⋊C8)C2312yes—
73C4⋊(C43⋊C8)C2312yes—
74#13063248—22no—
75#13063246—21no—
76#13063246—21no—
77#13063245—22no—
78#13063245—21no—
79#13063245—21no—
80C4×C43⋊C8—22no—
81C4×C43⋊C8—22no—
82C4×C43⋊C8D411yescharacteristic
83C4×C43⋊C8D411yescharacteristic
84C4×C43⋊C8C2311yescharacteristic
85C4×C43⋊C8C2311yescharacteristic
86C2×#41×C43—21no—
87C22×Q8×C43D411yescharacteristic
88#137×C43—44no—
89C2×Q16×C43—22no—
90C2×SD16×C43—22no—
91C2×M16×C43—21no—
92C4⋊Q8×C43C2311yescharacteristic
93#127×C43C2311yescharacteristic
94#124×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43D412yes—
100C4×Q8×C43C2312yes—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109#103×C43—22no—
110#102×C43—22no—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×Q8×C43—22no—
115C2×Q8×C43—21no—
116C2×Q8×C43D814yescomplemented
117C2×Q8×C43C2×D412yes—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C2×C22⋊D43—41no—
129#10621898—42no—
130#10621898—42no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×C4×D43—41no—
135C2×Dic86—21no—
136Q16×C43—44no—
137SD16×C43—44no—
138M16×C43—42no—
139C2×C8×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43C2×D412yes—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C42×C43—22no—
149C42×C43—22no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154#10621885—44no—
155#10621884—44no—
156#10621882—42no—
157#10621882—42no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162#10621877—42no—
163C2×C43⋊C8—22no—
164C2×C43⋊C8—22no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—41no—
167C2×C43⋊C8—42no—
168C2×C43⋊C8C2×D411yescharacteristic
169C2×C43⋊C8C2×D411yescharacteristic
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172C23×C43—41no—
173C23×C43#12111yescharacteristic
174C22×D43—41no—
175Q8×C43—22no—
176Q8×C43—24no—
177Q8×C43—41no—
178Q8×C43—41no—
179Q8×C43C2×D814yes—
180D4×C43—41no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—81no—
185D4×C43—82no—
186C2×C4×C43—22no—
187C2×C4×C43—24no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—22no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—41no—
194C2×C4×C43—82no—
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43C2×D812yes—
199C2×C4×C43#13512yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C2×#4111yescharacteristic
203C22⋊D43—82no—
204C2×Dic43—41no—
205D172—41no—
206D172—41no—
207D172—41no—
208D172—41no—
209D172—81no—
210C4×D43—82no—
211Dic86—41no—
212Dic86—41no—
213C8×C43—42no—
214C43⋊C8—21no—
215C43⋊C8—21no—
216C43⋊C8—21no—
217C43⋊C8—42no—
218C43⋊C8—42no—
219C43⋊C8#13712yescomplemented
220#19261—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43#46612yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—24no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—42no—
236C4×C43—81no—
237C4×C43#46612yes—
238C4×C43C22×D811yescharacteristic
239C4×C43C2×#13511yescharacteristic
240C4×C43C2×#13711yescharacteristic
241C4×C43#57511yescharacteristic
242Dic43—81no—
243#3169—431no—
244#3037—431no—
245#3037D4311yescharacteristic, complemented
246C2×C8×Q8—431no—
247#1682—432no—
248#1682—432no—
249#1674—432no—
250#1668—432no—
251#1567—431no—
252#1547—431no—
253#1547—431no—
254C2×C43—22no—
255C2×C43—161no—
256C2×C43#303711yescharacteristic
257C2×C43C2×#46611yescharacteristic
258C2×C43#306711yescharacteristic
259D43—161no—
260C2×#137—21no—
261C2×#137—861no—
262#532—431no—
263#532C2×D4311yescharacteristic
264C2×C4×Q8C2×D4311yescharacteristic
265#500—431no—
266#493—431no—
267#486—431no—
268#486—431no—
269#466—861no—
270#466—861no—
271#464—22no—
272#464—862no—
273#462—432no—
274#462C2×D4312yes—
275#460—432no—
276#460C2×D4312yes—
277C8×Q8—432no—
278C8×Q8—432no—
279C8×Q8—861no—
280C8×Q8—861no—
281C4×D8—861no—
282C4×D8—861no—
283#423—431no—
284#423C2×D4311yescharacteristic
285C2×C4⋊C8—431no—
286C2×C4⋊C8—861no—
287#417—21no—
288#417—861no—
289C2×C4×C8—431no—
290C2×C4×C8—861no—
291#335—432no—
292#335—432no—
293#332—432no—
294#332—432no—
295#331—432no—
296#331—432no—
297C43#1926111yescharacteristic, complemented, Sylow
298C2×#41—21no—
299C2×#41—861no—
300C22×Q8C22⋊D4311yescharacteristic
301#137—44no—
302#137—1724no—
303C2×Q16—22no—
304C2×Q16—862no—
305C2×SD16—22no—
306C2×SD16—862no—
307C2×D8—861no—
308C2×D8—861no—
309C2×M16—21no—
310C2×M16—861no—
311C22×C8—431no—
312C22×C8—431no—
313C22×C8—861no—
314C4⋊Q8—431no—
315C4⋊Q8C22×D4311yescharacteristic
316#127—431no—
317#127C22×D4311yescharacteristic
318#124—21no—
319#124—861no—
320#121—21no—
321#121—21no—
322#121—861no—
323#121—861no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8C22⋊D4312yes—
327C4×Q8C22×D4312yes—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—861no—
331C4×D4—861no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C22⋊D4311yescharacteristic
334C2×C42—21no—
335C2×C42C22×D4311yescharacteristic
336#107—861no—
337#107—861no—
338C4⋊C8—21no—
339C4⋊C8—432no—
340C4⋊C8—432no—
341C4⋊C8—862no—
342C4⋊C8—862no—
343C4⋊C8—861no—
344C4⋊C8—861no—
345C4⋊C8C22×D4312yes—
346#103—22no—
347#103—862no—
348#102—22no—
349#102—861no—
350#102—861no—
351#102—861no—
352#102—861no—
353#102—862no—
354C4×C8—431no—
355C4×C8—431no—
356C4×C8—431no—
357C4×C8—431no—
358C4×C8—862no—
359C4×C8—862no—
360#41—42no—
361#41—42no—
362#41—1722no—
363#41—1722no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—21no—
367C2×Q8—861no—
368C2×Q8#1062188214yescomplemented
369C2×Q8C2×C22⋊D4312yes—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—861no—
375C2×D4—861no—
376C2×D4—861no—
377C2×D4—1721no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—1721no—
382C22×C4D4×D4311yescharacteristic
383C22×C4#1062190011yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385Q16—44no—
386Q16—1724no—
387SD16—44no—
388SD16—1724no—
389D8—1722no—
390D8—1722no—
391M16—42no—
392M16—1722no—
393C2×C8—22no—
394C2×C8—431no—
395C2×C8—431no—
396C2×C8—431no—
397C2×C8—431no—
398C2×C8—862no—
399C2×C8—862no—
400C2×C8—862no—
401C2×C8—1721no—
402C2×C8—1722no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4C2×C22⋊D4312yes—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C42—22no—
416C42—22no—
417C42D4×D4311yescharacteristic
418C42#1062190011yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—41no—
422C23—1721no—
423C23#1306329711yescharacteristic
424Q8—24no—
425Q8—22no—
426Q8—41no—
427Q8—41no—
428Q8—1721no—
429Q8—1721no—
430Q8C2×#1062188214yes—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—81no—
436D4—82no—
437D4—3441no—
438D4—3442no—
439D4—1721no—
440D4—1721no—
441D4—1721no—
442D4—1721no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—82no—
452C2×C4—3442no—
453C2×C4—1721no—
454C2×C4#1306329711yescharacteristic
455C2×C4#1306329711yescharacteristic
456C2×C4#1306329711yescharacteristic
457C2×C4C2×#1062188212yes—
458C2×C4#1306334512yes—
459C2×C4C2×D4×D4311yescharacteristic
460C2×C4C22×C22⋊D4311yescharacteristic
461C2×C4C2×#1062190011yescharacteristic
462C8—42no—
463C8—432no—
464C8—861no—
465C8—861no—
466C8—861no—
467C8—1722no—
468C8—1722no—
469C22—21no—
470C22—21no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—3441no—
475C22—3441no—
476C22—3441no—
477C22#1458313312yes—
478C22C2×#1306329711yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—24no—
483C4—42no—
484C4—81no—
485C4—3441no—
486C4#1458313312yes—
487C4C22×#1062188211yescharacteristic
488C4C2×#1306334511yescharacteristic
489C4#137×D4311yescharacteristic
490C4#1458369811yescharacteristic
491C2—22no—
492C2—161no—
493C2—6881no—
494C2#1914406411yescharacteristic
495C2C2×#1458313311yescharacteristic
496C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3037C2
socleC22×C43C2×#121
prime radical#19145170C2
hypercenter#3037D43
hypocenterC43#19261
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #19144067C2semidirect
3. C2×Q8×C43⋊C8C2semidirect
4. #19134041C2semidirect
5. #19134037C2semidirect
6. #19133987C2semidirect
7. #19133953C2semidirect
8. #19133353C2semidirect
9. #19133273C2semidirect
10. #19133272C2semidirect
11. C43×#3037C2semidirect
116. C2×Q8×C43D8semidirect
219. C43⋊C8#137semidirect
245. #3037D43semidirect
297. C43#19261semidirect
368. C2×Q8#10621882semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191440672
C2×Q8×C43⋊C82
#191340412
#191340372
#191339872
#191339532
#191333532
#191332732
#191332722
C43×#30372
#1926143